4G Mobile and Wireless Communications Technologies 8792329020, 9788792329028

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4G Mobile & Wireless Communications Technologies

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4G Mobile & Wireless Communications

Technologies Sofoklis

Kyriazakos

Aalborg University Ioannis Soldatos Athens Information Technology

Technology

George Karetsos Research Center of Thessaly

Routledge

Taylor & Francis Group LONDON AND NEW YORK

Published 2008 by River Publishers River Publishers Alsbjergvej 10, 9260 Gistrup, Denmark www.riverpublishers.com

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4G Mobile & Wireless Communications Ioannis Soldatos,

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To our lovely wives, that took over our wedding preparations while we were busy with this book!

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Preface

Mobile and wireless communications are moving towards a new era that will be characterized by the seamless collaboration of heterogeneous systems, the need for high speed communications while on the move and for advanced services with quality guarantees. Recent market research studies show that most of the traffic in the future wireless networks will be produced by mobile multimedia services which are expected to proliferate by the year 2010. On the other hand mobile and wireless communications technology is becoming more and more important in developing countries where people demand fast deployment and low cost for broadband wireless internet services. The objective of this volume is to gather research and development on topics shaping the fourth generation (4G) in mobile and wireless communications and reveal the key trends and enabling technologies for 4G. We envisage 4G wireless communication systems as IP based solution providing integrated services (voice, data, multimedia) regardless of time and end-users’ location. 4G technologies will manifest the benefits of the wireless and wired technologies convergence, through enabling a wide range of innovative (both indoor and outdoor) applications. 4G applications will feature premium quality, high security and an affordable cost. The vision, though fantastic, is associated with a host of technical and technological challenges. A great deal of the later are discussed in the articles of this volume, which aims at providing insights on the research issues and solutions that are directly associated with leading edge 4G technologies and services. Taking into account recent developments in the world of wireless communications we have given emphasis to cover all these technologies and aspects that are considered as cornerstones for achieving the goals set for 4G and that will further boost research and development of next-generation mobile communications.

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About the Editors

was born in 1975 in Athens. He graduated Athens 1993 and studied Electrical College Engineering and Telecommunications in RWTH Aachen, Germany. Then he moved to the National Technical University of Athens, where he obtained his Ph.D. in Telecommunications in 2003. He also received an MBA degree in Techno-economic systems from the same university. He has more than 60 publications in international conferences, journals, books and standardization bodies. He has been invited as reviewer, chairman, member of the committee, panelist and speaker in many conferences and he has served as TPC chair in 2

Dr.-Ing. Sofoklis Kyriazakos

International conferences. Currently he holds the academic position of Assistant Professor in the University of Aalborg. Sofoklis has managed, both as technical manager and coordinator, a large number of multi-million Telecom and IT projects in NTUA. During the last seven years he also worked as external consultant in the area of Telecommunications. In 2006 he founded Converge S. A., an ICT company that is member of the PRC Group, that he is now the Managing Director. Prof. John Soldatos , PhD (born in Athens. Greece in 1973) obtained his Bachelor/MSc degree in 1996 and his Phd in 2000, both from the ECE Department of the National Technical University of Athens (NTUA). Dr. Soldatos has had an active role (wp-leader, technical manager, project manager) in more than 20 European Commission co-funded research projects. He has also considerable experience (senior developer, IT systems architect, team leader, technical project manager) in several enterprise projects, where he worked for many leading Greek enterprises. Furthermore, he has been involved in several large scale industry projects as a principal IT consultant. As a result of his research activities he has co-authored more than 110 papers published in international journals and conference proceedings, while he has co-edited two books and two journal special issues. His current research interests are in Pervasive, Grid and Autonomic Computing, as well as Broadband Networking. Dr. Soldatos has attracted (as principal investigator) multi-million euro research grants in all these areas. He also serves as a reviewer in major journals, as an evaluator for EU projects/proposals and business plans, while he has also served as organizing chair, tutorial chair, and TPC member in conferences. Recently, he served as TPC co-chair of the IEEE PIMRC07 conference. Dr. Soldatos is with Athens Information Technology ( AIT) since March 2003, where he is currently an Associate Professor.

numerous

Prof. George T. Karetsos was born in Karditsa, Greece in 1968. He received his diploma in electrical and computer engineering in 1992 and his Ph.D. in

telecommunication systems in 1996, both from the National Technical University of Athens, Greece. He is currently an associate professor in the Information Technology and Telecommunications Department of the Technological Educational Institute of Larissa, Greece and a research associate at the Technological Research Center of Thessaly (TRC-T), Greece. He has participated in many European and national research projects dealing with the optimization of protocols and operations as well as the efficient design and management of advanced services in fixed and wireless networks. He was the TPC co-chair of European Wireless 2006 conference and he has served as a member of technical committees and as a reviewer for various international conferences and journals. His research interests are in the areas of active networking, nomadic computing, performance evaluation, and resource management for fixed and wireless networks.

Table of Contents

List of Abbreviationsxv

1 Introduction

1: Radio Resource Management (RRM) Sofoklis Kyriazakos5

Part

Dynamic

and

Quality of Service (QoS)

Channel Allocation in IEEE 802.11

Jiayuan Chen, Sverrir Olafsson and Xuanye Gu9 An Overview of

Peak-to-Average Power Ratio Reduction Techniques

for OFDM

Systems Yeong-Luh Ueng and Shih-Kai Lee23

Mobile Ad Hoc Networks: Challenges and Solutions for Quality of Service Assurances Lajos Hanzo (II.) and Rahim Tafazolli35

Providing

Cell Sizing Scheme for Asymmetric Traffic Accommodation in CDM A/FDD Cellular Packet Systems

Adaptive

Kazuo Mori49 A

Dynamically Self-organized Clustering

Protocol for Mobile

Ad Hoc Networks Chung-Hsien Hsu and Kai-Ten Feng 61

Opportunistic Scheduling in Load Perspective Yahya S. Al-Harthi75

Wireless Networks: A Feedback

Cross-Layer Optimization for Upstream TCP Flows in IEEE 802.11 Wireless LANs Nakjung Choi, Jiho Ryu, Yongho Seok, Taekyoung Kwon and Yanghee Choi87

Communication for Energy Efficient Wireless Sensor Networks 97 Ljiljana Simić, Stevan M. Berber and Kevin W. Sowerby

Cooperative

Cross-Layer Optimization with Guaranteed QoS Wireless Multiuser OFDM Systems

for

Nan Zhou, Xu Zhu and Yi Huang 109

Handling Issues in DVB-H Systems 121 Araniti, Antonio leva, Antonella Molinaro

Handover

Giuseppe

Part 2: Channel Modelling, MIMO and OFMD George T. Karetsos131

Adaptive Dania

OFDMA

Systems

Marabissi, Daniele Tarchi,

Romano Fantacci135

Bounds and Algorithms for Data-Aided Channel Estimation in OFDM Heidi Steendam and Marc Moeneclaey 149 Distributed Space-Time Block Relay Terminals 159 Ryosuke UCHIDA

Coding for Large Set of

Comparison Between Parametric and Nonparametric Channel Estimation for Multipath Fading Channels Dieter Van Welden, Frederik Simoens, Heidi Steendam and Marc Moeneclaey 169

A

Envelope Correlation Analysis of MRC Signals in Correlated Rician Fading Zhuwei Wang, Xin Zhang 179

Experimental Investigation of Channel IEEE802.11b WLAN System

Estimation for

Yu Imaoka, Hiroshi Obata, Yohei Suzuki, and Yukitoshi Sanada 189

Hybrid-ARQ Techniques Dheeraj Sreedhar201 Multiuser

Diversity in

and its

MIMO

213 Xing ZHANG, Wenbo WANG

Application in 4G Wireless Systems

Systems: Theory

and Performance

On MIMO Channel Characterization for Future Wireless Communication Systems H. Farhat, R. Cosquer, G. El Zein 225

Modelling and Analysis of Capacity-Optimal Indoor Line-Of-Sight Wireless Channels Christian A. Hofmann and Andreas Knopp 235 Design of Compact Antenna Arrays for MIMO Communications Yuanyuan Fei and John

MIMO

Wireless

Thompson247

Error Correcting Codes and Iterative Decoding 257 Massinissa Lalam, Karine Amis and Dominique Leroux

Space-Time

Performance Evaluation of MIMO Multiuser Schemes under QoS Requirements 267 Nizar Zorba and Ana I. Pérez-Neira

Opportunistic

Part 3: Applications Services and Business Models 281 John Soldatosa Metric Multidimensional Scaling for Localization and Tracking Davide Macagnano, Giuseppe Destino and Giuseppe Abreu 285 Localization in Ad Hoc Networks for Mobile Service Provisioning 295 Yong Bai, Lan Chen

Ubiquitous

Human Body Detection using UWB-IR Indoor Channel 305 Keiji TERASAKA and Akihiro KAJIWARA An Overview of Wireless M AC Protocols for

Vehicular Communications

Spyridon Vassilaras, Spyros

Tsevas and

Gregory

S. Yovanof 317

WiMedia UWB Concept, Design and Implications Karsten Schoo, Harold Kaaja, Janne Marin and Juha Salokannel329 —

Signalling Model of Service Discovery in Heterogeneous Personal Networks

Thafer H. Sulaiman,

Hikmat Aldelo and Hamed S.

Al-Raweshidy 341

A Business Model for QoS Assessment in Mobile Wireless Networks 351 Francesco Benedet to and Gaetano Giunta

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List of Abbreviations

ABBREVIATION MEANING 3G Third Generation AC Admission Control AMC Adaptive Modulation and Coding AWGN additive White Gaussian noise BER Bit Error Rate BER Bit error Rate BLER Block Error Rate BS Base Station BS Base station CAC Call Admission Control cdf cumulative distribution function CDF Cumulative Distribution Function CDT Cell Description Table CRB Cramer Rao Bound CRB Cramer-Rao lower bound CSI Channel State Information CSMA/CA Carrier-sense multiple access with collision avoidance CTS Clear To Send DA Directory Agent DCF Distributed Coordination Function DCF Distributed Coordinated Function DCT Discrete Cosine Transform DSR Dynamic source routing DVB Digital Video Broadcasting DVB-C Digital Video Broadcasting-Cable DVB-H Digital Video Broadcasting-Handheld DVB-S Digital Video Broadcasting-Satellite DVB-T Digital Video Broadcasting-Terrestrial ES Elementary Stream FDD Frequency division Duplexing (I)FFT (Inverse) Fast Fourier Transform i.i.d. independent and identically distributed IDCT Inverse Discrete Cosine Transform IEEE Institute of Electrical and Electronics Engineers INT IP/MAC Notification Table

IP Internet Protocol LAN Local Area Network MAC Medium Access Control MAC Media Access Control MAC Medimum Access control MAC Medium Access Control MANET Mobile Ad Hoc Network Modultation MER Error Ratio MFN Multi-Frequency Network MIMO Multiple Input Multiple Output Maximum ML Likelihood Multibeam MOB Opportunistic Beamforming MPE Multi-Protocol Encapsulation MPE-FEC Multi-Protocol Encapsulation Forward Error Correction Pictures Moving MPEG Experts Group —

MPEG-2 Pictures Experts Group-2 Moving M-QAM M-ary Quadrature Amplitude Modulation MSE Mean Squared Error MSE mean squared error MSE Mean Square Error

Network NIT Information Table Orthogonal OFDM Frequency Division Multiplexing Orthogonal OFDM Frequency Division Multiplexing OFDM Orthogonal Frequency division Multiplexing Orthogonal OFDM Frequency Division Multiplexing OFDMA Orthogonal Frequency Division multiple Access Peer-to-Peer P2P PAT Association Table Program PES Packetized Elementary Stream PHY Physical

Packet PLR loss ratio PMT Program Map Table PN Personal Network Pseudo-Random PN Noise PSI/SI Program Specific Information/Service Information Packet PSR Success Rate QAM Quadrature Amplitude Modulation QCIF Common Intermediate Format Quarter QoS of Quality Service QoS of Service Quality QoS Quality of Service QoS of Service Quality QoS Quality of Service Phase Shift Keying Quadrature QPSK

QPSK RF RN RSSI RTS SA SD SDH SFN SINR SNIR SNR SNR SNR SNR TCP TDD TDMA TPS TS UA UHF UMTS UMTS UMTS VANET VHF VoIP WiMAX WLAN WLAN

Quadrature Phase shift Keying Radio Frequency Reference Node Received Signal Strength Indicator Request To Send Service Agent Service Discovery Segmentation-aided and Density-aware Hop-count Single-Frequency Network Signal-to-interference-noise ratio Signal to Noise and Interference Ratio Signal Noise Ratio Signal to Noise Ratio Signal To noise ratio Signal to Noise Ratio Transmission Control Protocol Time division duplexing Time Division Multiple Access Transmitter Parameter Signalling Transport Stream User Agent Ultra High Frequency Universal Mobile Telecommunications System Universal Mobile Telecommunications Systems Universal Mobile Telecommunications System Vehicular ad hoc network Very High Frequency Voice over IP Worldwide Interoperability for Microwave Access Wireless local area network Wireless Local Area Network

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Introduction

Mobile and wireless communications are moving towards a new era that will be characterized by the seamless collaboration of heterogeneous systems, the need for high speed communications while on the move and for advanced services with quality guarantees. Recent market research studies show that most of the traffic in the future wireless networks will be produced by mobile multimedia services which are expected to proliferate by the year 2010. On the other hand mobile and wireless communications technology is becoming more and more important in developing countries where people demand fast deployment and low cost for broadband wireless internet services. The objective of this volume is to gather research and development on topics shaping the fourth generation (4G) in mobile and wireless communications and reveal the key trends and enabling technologies for 4G. We envisage 4G wireless communication systems as IP based solution providing integrated services (voice, data, multimedia) regardless of time and end-users’ location. 4G technologies will manifest the benefits of the wireless and wired technologies convergence, through enabling a wide range of innovative (both indoor and outdoor) applications. 4G applications will feature premium quality, high security and an affordable cost. The vision, though fantastic, is associated with a host of technical and technological challenges. A great deal of the later are discussed in the articles of this volume, which aims at providing insights on the research issues and solutions that are directly associated with leading edge 4G technologies and services. Taking into account recent developments in the world of wireless communications we have given emphasis to cover all these technologies and aspects that are considered as cornerstones for achieving the goals set for 4G and that will further boost research and development of next-generation mobile communications. The book is organized in tree sections, namely: • Section 1 — Radio Resource Management and Quality of Service • Section 2 — Channel Modelling, MIMO and OFMD • Section 3 — Applications Services and Business Models In particular the following matters are extensively covered in individual chapters: • Dynamic Channel Allocation in IEEE 802.11 • Peak-to-Average Power Ratio Reduction Techniques for OFDM Systems

DOI: 10.1201/9781003336853-1

Introduction • •

•

• •

• •

• • • • •

• •

• • •

•

• • •

Mobile Ad Hoc Networks Adaptive Cell Sizing Scheme for Asymmetric Traffic Accommodation in CDMA/FDD Cellular Packet Systems Dynamically Self-organized Clustering Protocol for Mobile Ad Hoc Networks Opportunistic Scheduling in Wireless Networks Optimizing Aggregate Throughput of Upstream TCO Flows over IEEE 802.11 Wireless LANs Cooperative Communication for Energy Efficient Wireless Sensor Networks Cross-Layer Optimization with Guaranteed QoS for Wireless Multiuser OFDM System Handover Handling Issues in DVB-H Systems

Adaptive OFDMA Systems Bounds and Algorithms for Data-Aided Channel Estimation in OFDM Distributed Space-Time Block Coding for Large Set of Relay Terminals Comparison Between Parametric and Nonparametric Channel Estimation for Multipath Fading Channels Envelope Correlation Analysis of MRC Signals in Correlated Rician Fading Experimental Investigation of Channel Estimation for IEEE802.1lb WLAN System Hybrid -ARQ Techniques and its Application in 4G Wireless Systems Multiuser Diversity in MIMO Systems: Theory and Performance MIMO Channel Characterization for Future Wireless Communication

Systems Modelling

and Analysis of Capacity-Optimal Indoor MIMO Line-Of-Sight Wireless Channels Design of Compact Antenna Arrays for MIMO Wireless Communications Space-Time Error Correcting Codes and Iterative Decoding Performance Evaluation of MIMO Multiuser Opportunistic Schemes under

QoS Requirements • •

• • • •

•

“Metric Multidimensional Scaling for Localization and Tracking” “Localization in Ad Hoc Networks for Mobile Ubiquitous Service

Provisioning” “Human body detection using

UWB-IR indoor channel” “An Overview of Wireless MAC Protocols for Vehicular Communications” “WiMedia UWB Concept, Design and Implications” “Signalling Model of Service Discovery in Heterogeneous Personal Networks” “A Business Model for QoS Assessment in Mobile Wireless Networks” —

While the above list of papers and topics is not exhaustive, it provides a thorough coverage of wide spectrum of topical research issues in 4G wireless communications. We strongly believe that these selected topics will be of great value for the

Introduction

future endeavors of researchers and practitioners in the fields of mobile and wireless communications. Finally we would like to thank all the authors for their contributions; without their support this book would not be possible.

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Radio Resource Management (RRM) and Quality of Service (QoS) Sofoklis Kyriazakosa a Aalborg University, Aalborg Abstract. This section encloses contributions of different authors that advance the state-ofart in several aspects of Radio Resource Management (RRM) and Quality of Service (QoS) in the area of 4G Mobile & Wireless Communications Technologies. Radio Resource Management covers a wide spectrum of technologies and aspects aiming to utilize systems' resources in an efficient manner by achieving maximum optimization. This can be applied to specific systems and Radio Access Networks (RANs), but it can also be system architectures to support cooperation among heterogeneous RANs achieving cross-network optimization. Quality of Service is the desired level of service required and is strongly linked with RRM. Quality of Service is defined in most of the times by set of Key Performance Indicators (KPIs) that measure the system’s performance.

the

Section Overview In the first

chapter, Jiayuan Chena, Sverrir Olafsson and Xuanye Gu present the Channel Allocation problem in single-hop 802.1 lb/g networks with multiDynamic in the form of hybrid Genetic Algorithm (GA) and Simulated APs. This is solved ple in a (SA) Annealing single-hop 802. lib network through a centralized manner. The authors present the DCA algorithm both for cellular networks and WLANs. Subsequently DCA based in heuristics is presented and the genetic algorithms and Simulated Annealing are discussed. A hybrid algorithm is proposed and simulation results are presented.

In the second chapter, an Overview of Peak-to-Average Power Ratio Reduction Techniques for OFDM Systems is presented by Yeong-Luh Uenga, and Shih-Kai Leeb. An overview of PAPR reduction techniques which is critical for OFDM systems, could be reduced by several techniques such as clipping, recursive clipping and filtering, algebraic coding, tone reservation, tone injection, active constellation extension, selective mapping, and partial transmit sequences. Chapter three focuses on Mobile Ad Hoc Networks: Challenges and Solutions for Providing Quality of Service Assurances. In this chapter, Lajos Hanzo and Rahim Tafazolli are raising the issue of QoS for Mobile ad hoc networks (MANETs), that have been envisioned to provide spontaneous, robust and ubiquitous communications services due to their decentralised operation and non-reliance upon existing network infrastructure. However, the mass deployment of MANET technology relies on quality of service (QoS )-sensitive applications being supported. The chapter attempts to provide a brief, but unique overview of issues affecting the provision of QoS assurances in M ANETs by mapping them directly to their effects on

the achievable QoS.

DOI: 10.1201/9781003336853-2

Radio Resource Management (RRM)and Quality of Service (QoS) Kazuo Mori in chapter four addressed an Adaptive Cell Sizing Scheme for Asymmetric Traffic Accommodation in CDMA/FDD Cellular Packet Systems and proposes its efficient scheme using an adaptive cell sizing technique. In the proposed scheme, each base station autonomously controls its coverage area so that almost the same quality can be provided across the service area under the asymmetric traffic conditions.

In chapter five, Chung-Hsien Hsu and Kai-Ten Feng present a Dynamically Self-organized Clustering Protocol for Mobile Ad Hoc Networks. This study focuses on cluster-based hierarchical routing algorithms that have been developed to increase the system performance. The control packets can be reduced in the cluster-based schemes due to the decreased numbers of mobile node that join the routing processes. However, the significant overhead resulting from the formation of the cluster structure make it unsatisfactory to assist the design of routing algorithms, especially with small number of communication pairs in the network. In this chapter, a dynamic clustering protocol is developed in order to alleviate the excessive overhead induced from conventional cluster formation. The cluster structure is simultaneously established along with the construction of the on-demand routing path. Yahya S. Al-Harthi presents in chapter six, an Opportunistic Scheduling in Wireless Networks: A Feedback Load Perspective. With the ability to track the channel at the transmitter, adaptive transmission can be performed. Such tracking can happen via a feedback from the receiver. In multiuser systems, as the number of who feedback their channel state information (CSI) increases, the spectrum that must be provisioned to carry this amount of feedback will create a large overhead on the system, which leads to an inefficient utilization of the bandwidth. In this chapter an opportunistic scheduling algorithm that schedules users based on their channels qualities is proposed. The proposed algorithm reduces the feedback load while preserving most of the performance of opportunistic scheduling. In order to reduce the feedback rate, quantized values indicating the modulation level are fed back instead of the full values of the signal-to-noise ratios (SNRs). users

resource

In chapter seven, Nakjung Choia, Jiho Ryua, Yongho Seokb, Taekyoung Kwona and Yanghee Choia present a Cross-Layer Optimization for Upstream TCP Flows in IEEE 802.11 Wireless LANs. The chapter revisits the interaction between MAC contention and TCP congestion control over IEEE 802.11 wireless LANs, misled in the previous efforts. A new scheme called TCP ACK Priority (TAP) in which, by allowing an access point to transmit TCP ACKs at the highest priority, an optimal number of competing stations are allowed to contend for media access to utilize link bandwidth efficiently. The ns-2 simulator is utilized to evaluate the performance of TAP with the IEEE 802.11 DCF. Ljiljana Simić, Stevan M. Berber and Kevin W. Sowerby present is chapter eight a Cooperative Communication for Energy Efficient Wireless Sensor Networks. The chapter shows that cooperative communication can be deployed in wireless sensor networks as an effective practical energy saving technique. In cooperative communication a partner node is recruited to help with communicating a source node’s message by overhearing and repeating it to the destination receiver. An energy analysis

Section Overview

of cooperation is presented to demonstrate that cooperative communication has the potential to significantly reduce the total energy cost of wireless communication, provided the transmission range is beyond a certain threshold. The feasibility of practically exploiting this energy saving potential is examined in a wireless sensor network by considering the energy savings achieved for a given source node cooperating with a range of potential partners, using optimal power allocation for the cooperative transmission. It is demonstrated that the partner choice region for energy efficient cooperation is large relative to the source destination separation, meaning that significant energy savings can be achieved in practice from cooperation with a wide range of partners. A simple distributed cooperation protocol for wireless sensor networks is presented, whereby each source node autonomously makes cooperation decisions based on a simple yet near optimally energy efficient cooperation strategy. In chapter nine a Cross-Layer Optimization with Guaranteed QoS for Wireless Multiuser OFDM Systems is presented by Nan Zhoua, Xu Zhua, and Yi Huanga. A novel cross-layer optimization scheme for the downlink multiuser orthogonal frequency division multiplexing (OFDM) system is presented with a proposed maximum weighted capacity (MWC) based resource allocation at the physical (PHY) layer that can provide a much better QoS than the previous resource allocation schemes, while maintaining the highest or nearly highest capacity and costing a similar complexity. In particular, the more fluctuation in different users’ data arrival rates, the more advantages of MWC in both QoS and capacity. In chapter ten, Giuseppe Aranitia, Antonio Ieraa, Antonella Molinaroa present Handover Handling Issues in DVB-H Systems. It is widely known that the DVB-H standard has been specifically conceived to deliver broadcasting content in a system characterized by a cellular coverage structure. In this chapter there are initially brief descriptions of main feature characterizing the DVB-H standard at the Physical and Data Link layers and then an overview of some of the most relevant proposal of handover handling algorithms and procedures. From this brief overview it clearly emerges that several issues relevant to handover management are still open, such as, for example, the choice of the measurement parameter used during the decision phase. Pros and contras of each alternative proposal are analyzed and, eventually, some hints are given in the view of the introduction of novel features, such as parameters estimation and active handoff. Overall this section addresses several aspects of RRM and QoS from different aspect views. These views vary from OFDM systems, MANET, DVB-H, Wireless Sensor Networks and WLANs. It is therefore obvious that both definitions need to consider a great number of parameters aiming to achieve cooperative RRM and increased QoS in a converging environment of 4G systems.

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Dynamic Channel Allocation in IEEE 802.11 Jiayuan Chena,b,1, Sverrir Olafssonb,c and Xuanye Gu b a University College London, United Kingdom b BT, Adastral Park, United Kingdom c University of Reykjavík, Iceland Appropriate channel selection for each Access Point (AP) is one of the major challenges in setting up and operating densely deployed 802.11 WLANs. The aim with the channel selection is to provide efficient reuse of spectrum and therefore minimize interference and improve users' quality of service. This chapter outlines essential background information about the Dynamic Channel Allocation (DCA) problem. A detailed overview of the state-ofthe-art thinking relating to this problemis addressedfrom cellular networks to Wireless Local Area Networks (WLANs). Based on a network model and problem formulation, the DCA problem is solved in the form of hybrid Genetic Algorithm (GA) and Simulated Annealing (SA) in a single-hop 802.11b network through a centralized manner. Abstract.

Keywords: Dynamic channel allocation, IEEE 802.11, Heuristics

1. DCA in Cellular Networks The channel allocation problem in general can be classified into two categories: Fixed Channel Allocation (FCA) and Dynamic Channel Allocation (DCA). In FCA, the set of channels are permanently allocated based on a pre-estimated traffic design [ 1 2 |. While in DCA, channels are allocated dynamically depending on current network conditions. Generally, DCA yields a better performance in terms of interference and throughput at the expense of an added complexity in the control ,

mechanism. The objective of the DCA is to effectively allocate the available channels to the APs such that the overall network performance can be maximized.

DCA schemes have been studied for cellular networks in the past few decades. Many researchers have proposed to formulate a cost function which evaluates a number of constraints violated by a given frequency assignment and then try to minimize this cost function. Channels in cellular networks are kept in a central controller called the channel pool. Each base station requests channels from this global channel pool based on its traffic load. As the total number of channels is limited, it requires that the same channel should be reused as much as possible.

1 Corresponding Author: Jiayuan Chen, Polaris 128, BT Adastral Park, Martlesham, Ipswich, IP5 3RE, UK.

DOI: 10.1201/9781003336853-3

Dynamic Channel Allocation in IEEE 802.11

Meanwhile, it is important to avoid interference between nearby users. Therefore, DCA in cellular networks can be formulated as follows [3]: min

(1) z

s period t period normal upper Sigma Underscript j equals 1 Overscript z Endscripts f Subscript i comma j Baseline times i element-of left-bracket 1 times comma n right-bracket

(2) |p q|≥ci,jp, q∈[1,z] (3) -

fi,j

=

0

or

1

j∈[l,z](4)

where z is the total number of channels required by the system, fi,j is a binary matrix shows the possible channel assignment. Vector D corresponds to the number of channels each cell required. Matrix C is compatibility matrix, it describes the minimum channel separation between cells i and j. p and q are the channels used in cell i and j. Therefore, the objective of DCA in cellular networks is to minimize the total number of channels required by the system, and at the same time, meet the channel demand for each cell expressed by Equation (2) and ensure that the resulting channel assignment does not lead to any interference between different calls in the same cell defined by Equation (3). Other alternative objective functions can be set as to minimize the call dropping or blocking probability. By investigating the already published approaches, DCA schemes can be implemented in a centralized or a distributed manner. In the centralized algorithms, a central controller is adopted to assign channels and assure that the required signal quality is maintained. While in distributed algorithms, any decisions are made regardless of the global status of the network. Therefore, in the case of the distributed algorithms, it is more difficult to predict whether they can achieve optimal channel assignment. The above channel optimization problem formulated by Equation (1) to (4) is known to be NP-hard [4 ], This means the time needed to compute an optimal solution increases exponentially with the size of the problem. Therefore, some heuristic assignment strategies such as Genetic Algorithm (GA), Simulated Annealing (SA). multi-coloring schemes and neural networks have emerged to deliver near optimal solutions. From these tools, GA [ 1 3 11 ] is categorized as an evolutionary strategy, which can be used to find a sub-optimal solution with relatively fast convergence speed. SA based approaches [ 12 13] achieve the global optimum asymptotically but with a slow rate of convergence and requires a carefully designed cooling schedule. Multi-coloring techniques [ 14 18] are usually used to find the minimal number of channels needed to satisfy a certain traffic load, while neural network heuristics [ 19 21 ] provide suboptimal solutions because they tend to converge to local optima. In spite of some similarities, distributed DCA has some obvious differences to the mutual exclusion problem. In distributed DCA, the decision on channel acquisition and release is taken by the associated base station according to the information from its own and several surrounding cells. As the decision is not based on the global status of the network, it can achieve suboptimal allocation as compared to the centralized schemes and may cause forced termination of ongoing calls. The authors -

,

,

-

-

2. DCA in WLANs of [22 25 ] realized the importance of preventing interference among nearby cells, thus adopted models and principles from mutual exclusion problem, established the relationship and more importantly emphasized the difference between these two problems. One of the main differences is that in standard mutual exclusion, two processes are not allowed under any circumstances to use the resource at the same time, but in distributed DCA the same channel can in fact be used simultaneously by several cells, what is not allowed is two (or more) cells within the minimum reuse distance doing so [25 ]. Based on their analysis, many researchers proposed tokenbased [26 28 ] and non-token based [29 31 ] algorithms to solve the distributed DCA based on mutual exclusion. Other works in designing distributed DCA [32 34 ] focus on maximizing channel reuse in various cells, which ensure that neighboring cells do not make conflicting decisions that may lead to interference between ongoing calls. All these works on DCA in cellular networks laid the foundation for the same problem to be solved in WLANs. -

-

-

-

2. DCA in WLANs As more and more IEEE 802.11 WLANs have been deployed to meet the growing demand for wireless data services, one challenging problem has arisen: How to efficiently and dynamically allocate the scarce radio spectrum to those APs? 2.1. Channel Configuration in 802.11b The DCA problem in WLANs is different from that of cellular system. This is mainly due to the different channel configurations for both systems. Figure 1 shows the channel configuration for 802.11b networks. Channels are represented by their centre frequency, starting from 2.412 GHz to 2.477 GHz, with up to 14 channels in total. Each channel is 22 MHz wide in order to accommodate a wireless signal. However, since channels are 5 MHz apart from each other, there are only three nonoverlapping channels — channel 1, 6 and 11. These channels can be used to transmit signals at the same time by neighboring APs without causing any interference. Overlapping channels can also be used for transmissions as long as the interference is calculated with channel overlapping coefficient. However, since the

Figure 1. IEEE802.11b channel configuration

off-the-shelf products only support three-channel configuration, most proposed schemes are mainly based on non-overlapping channels. 2.2. Motivations and Challenges According to the channel configuration, it is obvious that the lack of nonoverlapping channels for simultaneous communication is one of the major difficulties in solving the DCA problem in 802.1 lb WLANs. Due to the limited number of usable channels, the signal coverage among many neighboring APs has to be overlapped. However, the channel contention among these neighboring APs results in worse performance than expected. Therefore, how to improve the network performance and reduce co-channel interference is one of the major problems in operating current IEEE 802.11 WLANs.

From another point of view, the increasing density of Wi-Fi APs is making this task even more challenging. This increment is due to their low cost and eases of deployment. Since the current 802.11 standards can support high data rate applications, it has led to the emergence of large scale WLANs in urban areas and enterprises. These spontaneous deployments by independent organizations are making the distances between APs and users as close as only a few meters away from each other [35]. This multi-AP network serving an even larger number of clients easily becomes a High-Density WLAN (HD-WLAN). In principle, HD-WLAN is a deliberate design choice for the enterprise or public network scenarios. As distances from clients to APs have been shortened, lower transmit power is more preferable to achieve high throughput compared with a sparse network with large power consumption. However, it also faces significant challenges due to the increased interference/contentions resulting from the close proximity between each AP. Although HD-WLAN initially emerged to eliminate the coverage holes, coverage is now often less of a concern because of the ubiquitous deployment of APs. Instead, scalable network capacity becomes a primary design challenge. 2.3. Literature Review Traditionally, static channel assignment has provided with respite from this problem. However, it is just a one-time approach and usually carried out in the installation phase. Network administrators first conduct a detailed RF site survey to find out the optimal number and AP locations to provide adequate coverage and performance for the users. Each AP will then scan all the available channels and select one with the least interference. It will stay in that channel until the next power on. This scheme can help prevent neighboring APs sharing the same channel initially. However, it cannot adapt to local environment changes and traffic conditions afterwards. Therefore, the current fixed channel assignments cannot provide the best performance for wireless networks. In [36] the classical vertex coloring approach has been modified to incorporate conflict set coloring and developed a centralized scheme for channel allocation in WLANs. It is worth pointing out that it is a static method, but runs periodically to

handle the dynamic system. The real difficulty of designing a dynamic scheme is to estimate the current network conditions. A centralized DCA strategy is proposed in [37] based on a real-time estimation of the number of active stations in the network. Then the authors develop a DCA scheme in MAC layer to minimize the throughput of the heavily loaded APs and maximize the channel utilizations considering the cochannel interference. This work is closely related to the well-known Bianchi model [38], but it is too complicated to implement. The previously mentioned works use centralized schemes to collect information from the entire network and derive the optimal or near-optimal configuration. Such approaches are not scalable due to the NP-hard nature of the problem and require a separate processing infrastructure for performing the centralized computation. As more and more network vendors are deploying their own networks, interfering APs will no longer belong to the same administrative domain, the centralized schemes are simply not feasible any more. Therefore, it is attractive to consider distributed DCA schemes in an unplanned network. The distributed DCA problem is very briefly addressed in [39 ], where APs are recommended to select an orthogonal channel that none of their neighbors has used. However, it was found to become instable and with limited performance gain in large networks. Authors in [40 ] proposed a fully distributed and self-managed algorithm with the aim of minimizing total interference. They model the network as a graph with links connecting neighboring APs. Each AP maintained a vector indicating the probability of using each channel. APs will confirm the channel assignment once the resulting interference is below a threshold. The authors of [40 ] claim that the rapid convergence can be guaranteed provided the number of required channels is no less than the chromatic number [41 ]. As the number of APs increases in the system, the major complexity of the algorithm is in computing this chromatic number, which presents a NP-complete problem. Kauffmann et al [42 ] develop an algorithm based on Gibbs sampler for channel selection and user association in WLANs. They construct a distribution function which dictates the channel selection made by each AP. It is complicated and computationally expensive as they consider the user association along with the channel selection.

Commercially, there are also several “spectrum management” products that are developed to automate channel assignment across WLANs. Some of them perform DCA based on current operating conditions fe.g. AutoCell [43 ] and Alcatel OmniAccess AirView Software [44 ]). Some of them also offer interference mitigation via transmit power control and load balancing. Unfortunately, due to their proprietary nature, very little is known about the design of the products and potential benefits.

3. DCA in WLANs Based on Heuristics All those works mentioned above provide a useful insight for investigating the DCA problems. In the following, we extend these works with specific focus on the HDWLANs. Two well-known optimization heuristics namely Genetic Algorithm and Simulated Annealing are adopted to solve the problem in a centralized manner.

Figure 2. Network model

3.1. System Model and Problem Formulation Figure 2 shows the system model of a HD-WLAN. It consists of seven randomly deployed APs and a group of wireless users. Each user is associated with its closest AP with the strongest received signal. As the Distributed Coordination Function (DCF) in WLANs is a contention-based medium access control (MAC) protocol, each AP can communicate with only one user at a time through its selected frequency channel.

To formulate the problem mathematically, in the following, the set of all APs is denoted by A, and the set of all available channels is denoted by C. |A| and |C| are the number of APs and number of available channels respectively. The matrix ρ: C × A →[0, 1] is defined in the following way, rho left-parenthesis i comma a right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column 1 2nd Column i f times up er A up er P times a times times u s e s times c h a n n e l times i 2nd Row 1st Column 0 2nd Column i f times up er A up er P times a times times d o e s times n o t imes u s e times c h a n n e l times i EndLayout

(5) where i ∈ {1,2,...,|C|}, a ∈ {1,2,...,|A|}. As each AP can only operate in one channel at a time, each column of p contains only one '1' and |C| —1 ‘O’.Ω |A|×|A| is an interference coefficient matrix. Ωab 1, if AP a and AP b use the same channel and 0 Gab, captures are within each other’s communication they range, otherwise Ωad the power loss on the path between AP a and b. Hence the interference experienced by AP a, operating on channel i, from its neighboring APs b with transmit power Pb, is given by Ia(i) Σb∈NB(a) ΩabGabPb + ηa, where NB(a) defines a local environment around the AP a but not including a itself, ηa is the background noise experienced by AP a. The objective of the DCA problem is to find a proper channel assignment, F (f1, f2,...,f|A|, such that the total interference TI is minimized: =

=

•

=

=

minmizeup erTup erIleft-parenthesi up erFright-parenthesi equalsnormalup erSigmaUnderscriptaepsilonup erAEndscriptsup erISubscriptaBaselinel ft-parenthesi fSubscriptaBaselineright-parenthesi equalsnormalup erSigmaUnderscriptfaepsilonup erCEndscripts imesnormalup erSigmaUnderscriptaepsilonup erAEndscripts imesnormalup erSigmaUnderscriptbepsilonup erNup erBleft-parenthesi aright-parenthesi Endscripts imesnormalup erOmegaSubscriptabBaselineSubscriptBaselineup erGSubscriptabBaselineup erPSubscriptbBaselineplusetaSubscriptaBaselinesubject onormalup erSigmaUnderscriptaequals1OverscriptSartAbsoluteValueup erAEndAbsoluteValueEndscripts imesnormalup erSigmaUnderscriptiequals1OverscriptSartAbsoluteValueup erCEndAbsoluteValueEndscripts imesrholeft-parenthesi com a right-parenthesi equalsStarAbsoluteValuenormalup erAEndAbsoluteValue

(6)

Figure 3. Solution representation, crossover, mutation operator and flow chart for GA

while in vector F each component fa can take any channel number value. The DCA problem has been proved to be NP-hard. In the following, we are going to use heuristics to solve this problem. 3.2. Introduction of Genetic Algorithm Genetic Algorithms (GA) are heuristics based on the idea of biological evolution. It is a population-based method and can deal with many solutions simultaneously. To use GA, one has to define the genetic representation of the solution domain and the fitness function to evaluate the solution quality. Figure 3(a) shows an example of a representation of solutions. There are seven APs in the system, the second string shows a possible channel assignment when only orthogonal channels can be chosen. The fitness value associated with each solution is the total interference in the system. During the evolution, new solutions are generated by using the genetic operators Crossover (Figure 3(b)) and Mutation (Figure 3(c)). Crossover takes place between two solutions, called Parents,by exchanging a part of their strings to form two new solutions, called Children.As for the analogy of GA in DCA, mutation means one of the APs randomly selects another channel for communications. Figure 3(d) shows the typical flow chart of GA. The procedure starts by generating an initial population of solutions. Then a loop is performed until some kind of termination criterion is reached. Most applications use the number of iterations or the stabilization of the population. Within the loop, new channel assignments are generated by recombination operators such as Crossover and Mutation. After that, these solutions will be further evaluated in terms of their fitness, which is the total interference in this case. Finally, the best assignments among the population are selected to form a new generation of solutions and a new iteration starts. 3.3. Introduction of Simulated Annealing Simulated Annealing (SA) is a generic probabilistic meta-algorithm for global optimization problems. The basic idea of SA comes from the physical process of annealing in metallurgy. In an annealing process, a solid is heated to a high temperature

and gradually cooled in order for it to crystallize. At high temperatures, the atoms move randomly and have high kinetic energy, but as they are slowly cooled they tend to align themselves in order to reach a minimum energy state. The principle of the SA technique lies in the following analogy between the physical process and DCA problem: feasible channel assignments are equivalent to the states of the solid, the energy of each state corresponding to the total interference for each assignment and the state with minimum energy being the optimal solution. SA uses a stochastic approach to direct the search. It guides the original local search method in the following way: if F is the present channel assignment in the system and TI[F] is the corresponding interference level, then a move to a new channel assignment F' is always accepted if it reduces the interference in the system, i.e. ΔTI TI[F'] TI[F] ≤ 0 If on the other hand the new channel assignment increases the interference level, it will be accepted with probability which depends on the change in interference and the current temperature, Pr[ΔTI,T] = exp(—ΔTI/T). It is this stochastic selection scheme helps SA to avoid in stuck a local optimum. getting The value of T varies from a relatively large value to a small value close to zero. These values are controlled by a cooling schedule which specifies the initial and present temperature at each stage of the algorithm. When the temperature is high, stochastic influence is strong, but as the temperature goes down the stochastic factor becomes less important. Therefore, the process gradually turns from stochastic behavior to more deterministic one. Finding the right cooling schedule is generally the most critical issue when using SA for optimization. Even though there are some theories suggesting how to decrease the temperature for some physical systems, this is not the case here under consideration. For this reason, we compared several cooling schedules and took fast cooling to be used here. —

=

.

3.4. Comparison between Genetic Algorithm and Simulated Annealing The characteristics of GA and SA are summarized in Table 1. Notice that, since both GA and SA are based on heuristics, the last feature of the algorithms stated in Table 1 is not always guaranteed. It only means GA may have high probability to be stuck in sub-optimal solutions, while SA is more likely to achieve global optima. In GA, its parallelized processing scheme evaluates several solutions at the same time, which consequently speeds up the algorithm. While in SA, the intelligent selection scheme provides a higher probability of finding an optimal Table 1. 1. Comparison between between Genetic Genetic Algorithm and and Simulated Simulated Annealing Table Genetic

Processing Method Centralized/Distributed

Convergence property Sub-optimality/optimality

Algorithm

Parallel Centralised Fast

Sub-optimality

Stimulated

Annealing

Sequential Distributed Slow Global Optimality

solution. Therefore, we combine them together to design a hybrid algorithm that provide a good trade-off between large computational time and local optimality.

can

3.5. Hybrid Algorithm The hybrid algorithm combines useful features from both GA and SA. It starts with a very high temperature T, and generates a large number of random solutions (initial population). Then Crossover and Mutation are applied to generate a new population. This is done as follows: 1. 2. 3.

4.

iteration, new offspring can be generated by Crossover of every pair of individuals. Afterwards Mutation is applied to each of the children, which is to randomly select channel for each AP. Evaluate each channel assignment in terms of integrated interference. If the new channel resulting in less interference, keep it for next generation. In one

Otherwise, accept it with a probability of min(l, exp(—Δ TI/T)). Slightly decreasing the temperature T according to the cooling schedule and then check if the termination is met. If it is, end the process, otherwise repeat step 1 to 3.

3.6. Simulations Evaluation In order to thoroughly assess the performance of the proposed algorithms, simulation networks are implemented in terms of different scales and topologies. All the scenarios have been simulated 1000 times to ensure accurate performance comparison. (a) Small Network Topology–7APs,3×7 Users We start with a small-sized system. In this experiment, there are 7 APs deployed in the area. Each of them is associated with 3 mobile users, which are randomly distributed. Figure 4 shows that all the algorithms can solve the DCA problem in WLANs for a small number of APs. The theoretical maximum average user SINR is 17.7dB, which occurred when no contending APs are sharing the same channel. Here SA achieves a solution closest to the optimum (17.6dB), but needs longer convergence time, while the hybrid algorithm has the fastest convergence speed. (b) Large Network Topology – 37 APs, 5×37 Users In order to evaluate the

algorithm’s capability to handle a large network, the number of APs is increased to 37 and each AP is associated with 5 users.

Figure 5 shows that all the algorithms take considerably more time to converge to the final state. The hybrid algorithm can handle large networks well in terms of

Figure 4. SINR performance in small networks

Figure 5. SINR performance in large networks

Figure 6. zoomed SA with longer evaluation time

the highest achievable SINR and the fastest convergence speed. Due to the sequential process mode of SA, it only shows its tendency to converge to the optimal solution but requires more time due to the large search space. Figure 6 shows a zoomed figure when we extend the simulation time up to 100000 iterations.

Figure 7. Standard deviation in small network

Figure 8. pdf in small network, at generation = 400

3.7. Statistical Analysis To assess the accuracy and suitability of each algorithm, we provide further statistical analysis. Two statistical measurements have been selected. One is standard deviation to indicate the accuracy of each algorithm in delivering the results. The other is probability density function (pdf), to provide statistical measure on how the data are distributed for different algorithms. (a) Small System–7APs,7×3 Users In Figure 7, SA has the lowest standard deviation when the algorithm converges, while in Figure 8 it has a very sharp peak compared with other two algorithms. This indicates that the solutions delivered by SA are narrowly distributed around the average SINR value. Therefore, SA appears to be the best choice to solve the problem within small systems. This result is consistent with the performance shown in Figure 5. (b) Large System – 37 APs, 37×5 Users When the system becomes larger the hybrid algorithm shows its superiority in terms of achieving steadier and lower standard deviation when the system converges as

Figure 9. Standard deviation in large networks

Figure 10. pdf in large networks, at generation = 1000

shown in

Figure 9. Figure 10 shows the pdf performance at final stage of each algorithm. We can see that the hybrid algorithm provides a slightly higher SINR performance. Therefore, we can conclude that the hybrid algorithm provides a better solution to solve the channel allocation problem for systems with a large number of multiple APs.

4. Conclusion The dynamic channel assignment to improve the efficiency of spectrum usage in WLANs has recently been studied by various authors. In the literature, some of the proposals focus predominantly on the static scheme, while the dynamic ones are found to either have limited performance gain or to be complicated to implement. In this chapter, we develop a framework of using Hybrid Genetic Algorithm and Simulated Annealing to solve the DCA problem in single-hop 802.11b/g networks with multiple APs. Extensive simulations have been carried out to validate the algorithm feasibility. Based on the simulation results and statistical analysis, the proposed hybrid algorithm appears to be able to provide a good trade-off between the convergence speed and the reaching of a near optimal solution.

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An Overview of Peak-to-Average Power Ratio Reduction Techniques for OFDM Systems Yeong-Luh Uenga, 1 and Shih-Kai Leeb a Department of Electrical Engineering, National Tsing Hua University, Taiwan b Department of Communications Engineering, Yuan Ze Univ., Taiwan Abstract. Orthogonal frequency-division multiplexing (OFDM) is a popular transmission technology for wireless broadband communication. Inherent high peak-to-average power ratio (PAPR), which is critical for OFDM systems, could be reduced by several techniques such as clipping, recursive clipping and filtering, algebraic coding, tone reservation, tone injection, active constellation extension, selective mapping, and partial transmit sequences. In this article, we shall give an overview of these PAPR reduction techniques. Keywords: Orthogonal frequency-division multiplexing (OFDM), Peak-to-average power ratio (PAPR).

1. Introduction Orthogonal frequency-division multiplexing ( OFDM ) is a well-known transmission technology for wireless broadband communication and has been employed in many applications such as DAB (Digital Audio Broadcasting), DVB (Digital Video Broadcasting). WLAN (Wireless Local Area Network), and WiMAX ( Worldwide Interoperability for Microwave Access). The problem of large peak-to-average power ratio (PAPR) of the time-domain OFDM symbol is a well-known disadvantage of OFDM technology. Consider a sequence of OFDM symbols in the time domain, i.e., s0(t),

symbol

s1(t + T), ···,sm(t + mT), ···. The baseband version of the m-th OFDM in the time domain, sm(t + mT), can be represented by up er S Superscript m Baseline left-parenthesis t plus m up er T right-parenthesis equals StartFraction 1 Over StartRo t up er N EndRo t EndFraction normal up er Sigma Underscript k equals 0 Overscript up er N negative 1 Endscripts up er X Subscript k Superscript m Baseline exp left-parenthesis j k times 2 pi times normal up er Delta f t right-parenthesis times 0 les -than-or-equal-to t les -than-or-equal-to up er T times

where j V—1, N is the number of subcarriers, Δf is the subcarrier spacing, T is the OFDM-symbol duration, and ais the complex baseband data to be modulated —

1 Corresponding Author: Yeong-Luh Ueng is with the Department of Electrical Eng. and the Institute of Communications Eng., National Tsing Hua University, Hsinchu, Taiwan, R.O.C. (email: [email protected]).

DOI: 10.1201/9781003336853-4

An Overview of Peak-to-Average Power Ratio Reduction Techniques on the k-th subcarrier in the m-th OFDM that the orthogonality can be achieved.

symbol.

It is

required

that

A=j

so

PAPR for the m-th OFDM symbol in the time domain is defined as: PAPnormalup erRSuperscriptmBaseline qualsStartSartFractionmaxUnderscript0les -than-or-equal-tonormalt es -than-or-equal-tonormalup erTEndscriptsStartAbsoluteValuesSuperscriptmBaselinel ft-parenthesi tplusmup erTright-parenthesi EndAbsoluteValuesquaredOverOverStartFraction1Overnormalup erTEndFractioni tegralSubscript0Superscriptup erTBaselineStartAbsoluteValuesSuperscriptmBaselinel ft-parenthesi tplusmup erTright-parenthesi EndAbsoluteValuesquared tEndEndFractionperiod

The OFDM time-domain signal consists of the summation of many subcarriermodulated signals. When the number of subcarriers is large, both the real part and imaginary part of the output signal at time t can be approximated as Gaussian distributed. That means high peak may arise occasionally. An extreme case is that all the subcarriers are modulated with all 1s’ by using binary phase shift keying (BPSK). Then, the peak power will be equal to N, while the average power is 1. The complementary cumulative distribution function (CCDF) is the probability Pr(PAPR >λ) which can be well approximated by (1 − (1 − e−λ)aN) if N is large enough, where λ is a positive constant and a = 2.8 [1]. Power amplifier (PA) is an important device for a communication system. Ideally, it is required to linearly respond to an input signal. The output signal is distortionless only if it is linearly related to the input signal. PA could not always linearly respond to an input signal if its instantaneous input power varies over a wide range unless a large OBO (Output BackOff) is employed. However, a large OBO will degrade the efficiency of the PA. Hence, the high PAPR problem of the OFDM time-domain signal will usually introduce distortion to the PA output signal. The signal distortion resulting from the PA non-linearity can be categorized to two classes, one is the AM-AM (Amplitude-to-Amplitude Modulation) distortion and the other is the AM-PM (Amplitude-to-Phase Modulation) distortion. Intermodulation distortion (IMD) resultant from the PA non-linearity will lead to out-of-band spectral expansion. This makes PA lineariziation more desirable. Due to the AM-AM non-linear distortion, an OBO value below the 1-dB compression point will usually be used to determine the PA operating point for maintaining enough linearity. We can use the method of predistortion to compensate the PA nonlinearity [2][3]. A straightforward idea of predistortion is to introduce an inverse function to the input signal before it enters into the PA. The predistortion can be implemented either by the RF circuits or by the baseband circuits. Recently, predistortion implemented on the baseband circuits is popular and is also called digital predistortion. Let the input signal be vi(t) = a(t) cos(wct + θ(t))

Then the corresponding PA output is given by vo(t) = G[a(t)] cos(wct + θ(t) + ψ[a(t)]),

where G[•] is the AM-AM characteristic function and ψ[•] is the AM-PM characteristic function. If the function of the digital predistorter is given by

1. Introduction

Figure 1. Digital predistortion block diagram.

F[a(t)] exp[jφ(a(t)], then the output of the predistorter is vd(t) = F[a(t)] exp[j(θ(t) + φ(a(t)))]

To compensate the PA non-linearity, two criteria must be satisfied, i.e., G[F[a(t)]] = λ a(t),

λ is a constant

φ(a(t)) + ψ(F[a(t)]) = 0

The adaptive digital predistortion circuits are composed by a complex gain adjuster, a LUT (Look-UP Table) to quantize the gain coefficients and an adaptive circuit block, which is responsible for deriving the aforementioned digital predistortion function, as shown in Figure 1. The predistortion function may be derived by using either a modulated signal input or a known training signal. The adaptive algorithms that are based on the use of a modulated signal employ statistical processing and typically require some curve fitting methods to generate a smooth predistortion function. The complexity of the adaptive algorithms can be significantly simplified by using a known training signal. As mentioned earlier, PA can be operated with a proper backoff to tackle the problem of high PAPR for OFDM systems [4]. However, PA with a large backoff leads to inefficient power usage. To avoid a large backoff of the amplifier, we must allow occasional signal distortion of the nonlinear amplifier or clip the signal before feeding it to the amplifier. Such arrangement will cause signal distortion (in-band distortion) and power spectral expansion (out-of-band emission) [1][4][5]. Hence, the techniques of PAPR reduction are required. The currently known PAPR reduction methods can be roughly divided into two categories, the redundancy based category and the distortion based category. The distortion based PAPR reduction methods include clipping [4 ][ 5 ][ 6 ] and recursive clipping and filtering (RCF) [ 7][ 8 ]. The redundancy based PAPR reduction techniques include algebraic coding [ 11]—[ 16], tone reservation and tone injection [ 17], active constellation extension (ACE) [ 18], selective mapping (SLM) [ 19]—[24 ], and partial transmit sequence (PTS) [25 ]-[ 32 ].

Figure 2. Block diagram of recursive clipping and filtering (RCF).

2. Techniques of PAPR Reduction 2.1. Clipping and recursive clipping and filtering (RCF) The simplest way of reducing PAPR is by clipping the time-domain OFDM signal [4], which will result in high in-band distortion and high out-of-band emission. These undesired distortions can be reduced by over-sampled digital clipping [6] and by digital filtering, respectively. However, if the high out-of-band distortion (emission) is filtered off, it is likely that the reduced PAPR of the clipped signal will regrow [5]. By repeating the same procedure several times, both low PAPR and low out-of-band emission can be achieved [7]. Such a method is called recursive (or repeated) clipping and filtering (RCF). The block diagram is shown in Figure 2 and the procedure is described as follows. Step 1 Append (L − 1)N zeros to X = (X0,X1, ···,XLN−1) . Then apply LNpoint IFFT on the zero-padded X to obtain the over-sampled time-domain signal x = (x0,x1, ···,xLN−1).

Step

2

ping

with

According a

to x,

clipping

perform

digital

clip-

ratio y1) to obtain where E is the operator of expectation.

x

Step

3

Apply LN-point

FFT

on

x

to

obtain the

frequency-domain signal

X1).

Step ∈i

LN {N,···,

4 Filter out the out-of-band emission of X 1} to obtain X.

by setting

X0 for

—

Step 5 Repeat Step 1 to Step 4 NIT times, where NIT is a positive integer. Although the out-of-band emission and the probability of the occurrence of high PAPR decreases, the error rate will increase as the number of recursions increases. The increased error rate is due to the increased in-band distortion.

In some cases, such as 16

under 3 dB backoff, the distortion of RCF of the un-coded system will remain above 10-4 significant In of the ratio. 8 regardless signal-to-noise [ ], a modified scheme called recursive clipand with bounded distortion (RCFBD) which can achieve effective ping filtering PAPR reduction while keeping distortion under control was proposed. RCFBD is the same as RCF except that additional constraint on the in-band distortion of each tone is applied during the recursive process of RCFBD. For coded OFDM systems, at the receiver, DAR (data aided reconstruction) [9 ][ 10] can be used to mitigate clipping noise and hence improve the error performance. is

so

that the

QAM/OFDM

error rate

2.2. Algebraic Coding In an OFDM system, different data sequences could result in time-domain signals with different PAPRs. For the purpose of reducing PAPR, it is clear that some data sequences resulting in high PAPRs should be excluded for transmissions. Appropri-

ately designing a coding scheme, which is with codewords other than these sequences, can effectively achieve PAPR reduction. In other words, these codewords forms the time-domain signals with low PAPR. Let an M-ary code C be a given set of N-tuples Xi). The aperiodic autocorrelation function (AACF) of a data vector X is defined as normal up er A Subscript normal up er X normal up er X Baseline left-parenthesi k right-parenthesi equals normal up er Sigma Underscript i Endscripts up er X Subscript Baseline Subscript i Baseline up er X Subscript i plus k Superscript asterisk

where * denotes a complex conjugate. The instantaneous power of x(t) can be expressed by normalup erPSubscriptnormalxBaselin left-parenthesi tright-parenthesi equalsStarAbsoluteValuenormalxeft-parenthesi tright-parenthesi EndAbsoluteValuesquared qualsStarFaction1Overup erNEndFraction ormalup erSigmatimesUnderscipt Endscriptsnormalup erSigmaUndersciptkEndscriptsup erXSubscript Baselin SubscriptBaselin up erXSubscriptkSupersciptaseriskBaselin eSupersciptjBaselin 2pileft-parenthesi minuskright-parenthesi normalup erDeltaf Baselin equals1plusStarFaction1Overup erNEndFractiontimesnormalup erSigmaUnderscipt Endscriptsnormalup erSigmaUndersciptlnot-equals0Endscriptsup erXSubscript Baselin up erXSubscript lus SupersciptaseriskBaselin eSupersciptminusjBaselin 2pilnormalup erDeltaf Baselin equals1plusStarFaction1Overup erNEndFractiontimesnormalup erSigmaUndersciptlnot-equals0UnderUndersciptEndscriptsnormalup erASubscriptu perXup erXBaselin left-parenthesi lright-parenthesi eSupersciptminusjBaselin 2pilnormalup erDeltaf

The AACF and the instantaneous power are obviously a Fourier pair. Consequently, if the AACF is impulse alike then the instantaneous power is nearly a constant and hence the PAPR is low. A famous relationship to a binary Golay complementary pair, X and Y, is defined as normal up er A Subscript normal up er X normal up er X Baseline times left-parenthesi k right-parenthesi plus normal up er A Subscript normal up er Y normal up er Y Baseline left-parenthesi k right-parenthesi equals StartLayout Enlarged left-brace 1st Row 1st Column 2 up er N comma 2nd Column f o r times k equals 0 2nd Row 1st Column 0 comma 2nd Column f o r times k not-equals 0 EndLayout

Any member of a Golay complementary pair is called a Golay sequence. We have Px(t) + Py(t) = 2

Since each instantaneous power is non-negative, it is concluded that Px(t) ≤ 2 and hence the peak power of a Golay sequence is at most 2. Owing to the average power of x(t) is P = 1, the PAPR is not greater than 3dB. The large set of binary length N = 2m Golay sequences can be obtained from certain Reed-Muller codes[15][16]. The research for finding coding structures of M-ary Golay sequences of various lengths is still on working. The disadvantage of using an algebraic coding to reduce PAPR is mainly on its low coding rate. Besides, an algebraic code with low PAPR is usually not optimal on its error correcting ability. 2.3. Tone Reservation Tone reservation (TR) is a kind of peak cancellation techniques. In an OFDM system, a tone means a subcarrier. Usually, most tones are used for carrying data and a few tones used as pilots for system synchronization or channel estimation. In addition to these tasks, some tones could be reserved for cancelling the peaks of an OFDM signal. As an easily understood example to describe the basic idea of tone reservation, we impose same reference symbol, say +1, on those reserved tones which are assumed to be contiguous. Those tones therefore form a sine signal after the IFFT. To shift the position of the sine signal to a peak of the OFDM signal and to scale (with or without changing sign) it up or down onto the OFDM signal can cancel the peak and reduce the PAPR. A shifting or a scaling of the sine signal is very easy when the operation is done on those tones in the frequency domain. Since there are several peaks of one OFDM signal, the operation can be repeated if the reserved tones are enough until all peaks are cancelled. In a formal notation, let the reference symbols imposed on L reserved tones are denoted as T where {i1,i···,2L}, are the subcarrier indexes of the reserved tones which are not necessarily to be contiguous. To solve the optimal value of Ti is a linear programming problem that can be determined by a gradient algorithm [ 17]. In wired systems, there are typically subcarriers with SNRs too low to send useful data. In such systems, the tone reservation method is very suitable for using these subcarriers to reduce PAPR without sacrificing the throughput. In wireless systems, there are however no fast feedback channel information to indicate which subcarriers are with low SNRs. The tone reservation method must use a pre-allocated set of subcarriers which may be with high SNRs to reduce PAPR. Therefore, the throughput is somewhat degraded.

2.4. Tone Injection and Active Constellation Extension The idea of tone injection (TI) is to increase the constellation size so that each point in the original constellation can be mapped to several equivalent points in the expanded constellation. Since each symbol in a data block is with more mapping choices, it is likely to achieve better PAPR performance. The method is called tone injection because substituting a point in the original constellation for a new point in the expanded constellation is equivalent to add a tone carrying the information

Figure 3. QPSK signal constellation.

of the vector between the two points. The tone injection method may introduce a power increase in the transmit signal due to the injected signal. Active constellation extension (ACE) is a similar PAPR reduction method to TI. In this method, some of the outer signal constellation points in a data block are allowed to move toward the outside of the original constellation. As explained by using a QPSK signal constellation, all the four points are outer points and allowed to move toward the extended shaded regions in Figure 3. Therefore, each symbol which is with more mapping choices makes the possible PAPR reduction and increases transmit signal power. Another advantage of this method is its possible lower BER because it provides additional noise margin when the outer signal points move to the extended regions. The ACE method can also be applied to a larger constellation size such as MPSK or MQAM. However, the usefulness of this method is rather restricted for a modulation with a large constellation size because the percentage of outer signal constellation points is decreased. It is possible to combine the TR and ACE methods to make the convergence of TR much faster.

2.5. Selective Mapping The selective mapping (SLM) technique maps each message into Q candidates and selects the candidate with the smallest PAPR for transmission. Fig. 4 shows an X(Q), are generated by mulimplementation ofSLM. Q candidates. X(1),X(2),..., B(Q). Under the tiplying X by Q statistically independent vectors B(1), B(2),..., assumption that the Q candidates are statically independent, the CCDF of PAPR is [1 (1 e-λ)aN]Q [19 ] Hence, the PAPR can be improved by selective mapping. There are two major issues associated with SLM. The first is that side information indicating the selected candidate should be transmitted to the receiver and erroneous decision of side information will seriously degrade the error performance. The second is that it requires a bank of IFFT to generate Q candidates in the original SLM [ 19]. This requirement usually increases the computational complexity significantly. —

—

In [20][22], coded OFDM systems which implement SLM without explicit side information were proposed. The degradation in error performance resultant from

Figure 4. Block diagram of an implementation of SLM.

incorrect side information is serious in [20 ] but is not observed in [22 ]. The transmission of side information will reduce the available bandwidth for user data. In [21 ][ 23 ], selective-mapping type PAPR-reduction techniques without using side information for turbo coded OFDM were proposed. Although side information is not needed in [21 ][ 23 ], the decoding complexity is increased.

There are some low-complexity SLM schemes in [24]. The basic idea in [24] is to produce Q candidate signals by using some conversion with only one IFFT output signal. The computational complexity of this conversion is lower than that of the Q IFFT operations. However, the number of candidates generated by this method is limited and the issue of side information is not dealt with. 2.6. Partial Transmit Sequences The basic idea of partial transmit sequences (PTS) is described as follows. An OFDM signal is formed by passing N data symbols through an IFFT device. Assume that these N data symbols are partitioned into M disjoint subblocks. Each subblock passes through an IFFT device can form a component signal. Actually the OFDM signal can be regarded as the combination of the M component signals since the operation of IFFT is linear. The component signals are called the “Partial Transmit Sequences". An OFDM signal with high PAPR is due to the constructive addition of these M component signals. To avoid the constructive addition and to have a better PAPR reduction, individual complex weighting factor, am, is introduced on each component signal before their combination as shown in Figure 5 where 1 ≤ m ≤ M. The complex weighting factor for the mth component signal is usually ,

= The factor with unit amplitude is to keep the only a phase rotation, i.e., am ejφm. signal the same power as the original OFDM signal. The values of these M weighting factors, {a1, a2, ···, are chosen so that aM} = {ejφe·1,jφM2·}, the peak power is minimal. It is possible to have an optimal CCDF of PAPR through an exhaustive search of all possible values of the M weighting phase factors. Usually, the selection of the phase factor is limited to a set with a finite number of

resultant

Figure 5. Block diagram of Partial Transmit Sequences.

elements, say φm ∈{θ|θ =W × 2π, for 1 ≤ q ≤ W}, for reducing the search complexity. As with SLM, the receiver must have side information about the generation of the OFDM signal, i.e., the chosen weighting factors.

3. Conclusion In this chapter, we have introduced some techniques for PAPR reduction. The distortion based PAPR reduction methods such as clipping and RCF are designed by trading distortion or error performance for PAPR reduction. We can achieve significant PAPR reduction by RCF. However, the degeneration in error performance is serious which can be mitigated by using the technique of decision-aided reconstruction [9][10]. The redundancy based PAPR reduction techniques such as algebraic coding, tone reservation, tone injection, ACE, SLM, and PTS are designed by trading bandwidth for PAPR reduction. The most elegant method is algebraic coding. However, the bandwidth efficiency is low for practical applications. The technique of tone reservation must use some pre-allocated subcarriers for PAPR reduction and hence the throughput is somewhat degraded. Tone injection and ACE can achieve PAPR reduction with power increase in transmit signal. SLM and PTS can achieve PAPR reduction with only a slight loss of bandwidth efficiency. However, the computational complexity is increased and the issue of side information should be dealt with.

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by Reed-Muller channel coding:

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C\ Taylor & Francis ~

Taylor&FrancisGroup http://taylo ra ndfra n ci s.com

Mobile Ad Hoc Networks: Challenges and Solutions for Providing Quality of Service Assurances Lajos Hanzo (II.)1 and Rahim Tafazolli University of Surrey, Guildford, UK Abstract. Mobile ad hoc

networks.(MANETs) have been envisioned to provide spontaneous,

robust and ubiquitous communications services due to their decentralised operation and nonreliance upon existing network infrastructure. However, the mass deployment of MANET technology relies on quality of service (QoS)-sensitive applications being supported. This

article first attempts

brief, but unique overview of issues affecting the provision by mapping them directly to their effects on the achievable QoS. In particular, QoS-aware routing and admission control (AC) are discussed and a new protocol extension is proposed to aid in answering the question of how well throughput assurances can be provided in highly dynamic MANET environments. We compare two approaches via simulation: that of pre-discovering and capacity-testing backup routes, and relying only on routes discovered during data session admission. The simulation results show that it is only worth proactively discovering and testing backup routes if the incurred overhead does not saturate the network. In this case, the vast majority of admitted data sessions can maintain their strict throughput requirements even in highly dynamic environments. of QoS

assurances

to

provide

a

in MANETs

Keywords: mobile ad hoc network (MANET), quality of service (QoS), admission control, routing.

1. Introduction From their roots in packet radio networks several decades ago [1], and through the research boom that began in the mid 1990s, much hope has been placed in mobile ad hoc networks (MANETs) [2] to provide spontaneous, robust and ubiquitous communications in areas where infrastructure is lacking. Of course a gateway node may provide Internet access, but MANET users are typically collaborators sharing messages and content with each other. Much-touted applications of MANETs include battlefield communications, disaster recovery, temporary gatherings such as conferences [1] and highly mobile vehicle-to-vehicle networks (VANETs) [3]. The developing world, where a larger proportion of people live in areas with limited infrastructure, could also benefit from MANET technology. In fact, the “One Laptop Per Child” project2 is set to deploy in various developing countries, to the best of our knowledge, the largest real-world MANET-like networks to date. The increase in interest in MANETs of the last 15 years or so was largely correlated with the increase in the capabilities and popularity of mobile devices and 1 Corresponding author: L. Hanzo, Centre for Communications Systems Research, University of Surrey, Guildford, GU2 7XH, UK. Email: [email protected]. 2 http://laptop.org/, accessed Nov. 8th, 2007.

DOI: 10.1201/9781003336853-5

Mobile Ad Hoc Networks

with the development of the 802.11 [4] standard (originally finalised in 1997) for wireless local area networks (WLANs). Most laptop computers and many personal digital assistants (PDAs) now come with 802.11-compliant air interfaces. With the option to operate them in ad-hoc mode, 802.11 is the primary MANET-enabling technology. Indeed, the majority of MANET research has assumed 802.11-based physical (PHY) and medium access control (MAC) layer solutions. We also focus on 802.11-based MANETs. In this article we assume that a typical MANET consists of a relatively large, but not huge number, say 10-100, of sophisticated mobile devices, such as laptop computers or personal digital assistants (PDAs). These devices have frequent access to battery-recharging facilities and are becoming increasingly powerful, thus energy, memory and processor power are not the most critical resources. In most works the most critical resource is considered to be the wireless channel capacity [5].

In Section 2, we discuss how characteristics of the MANET environment affect the achievable QoS, and overview proposed solutions. In Section 3, we focus on routing and admission control (AC) for providing an assured throughput service in highly mobile networks. We compare the performance of two approaches via simulation and discuss the results. Finally, conclusions are offered along with future work directions in Section 4.

2. Provision of QoS Assurances in MANETs While research efforts are on-going, and performance improvements in particular scenarios may be readily attained, existing solutions for providing best-effort services in MANETs are generally adequate. However, if MANETs are to gain mass appeal, they must support QoS-sensitive multimedia applications. The issues and challenges concerning the provision of QoS assurances in MANETs have been discussed extensively (e.g. [5], [6]), although the existing overviews tend to focus on how protocol operation is affected. By contrast, we attempt to map the issues and their solutions at various layers directly to how they affect applications’ experienced QoS. While QoS-aware protocols have received substantial research attention [5], [7], [8], there is still a long way to go until MANETs can adequately support today’s QoS-sensitive applications. The most important QoS metrics from the applications’ point of view are endto-end throughput, packet delay, delay jitter and packet loss ratio (PLR) [ 7]. These metrics are largely governed by three factors: the wireless channel’s quality, its capacity relative to the traffic load and node mobility. While the effects of these factors span protocol layers, we attempt to discuss them in a layered manner for the sake of clarity. 2.1. Physical Layer Issues The 802.11-2007 standard[4 ] specifies physical data rates rangingfrom 1Mbps up to 54Mbps, in the 5Ghz band (what used to be 802.11 a) or the 2.4Ghz band. The newest

2. Provision of QoS Assurances in MANETs

layer amendment, 802.11n [ 9], will provide data rates up to 100Mbps. However, depending on the propagation environment, the wireless channel is typically unreliable, especially for mobile nodes. Shadowing and fast-fading-induced received signal power fluctuations [ 10] may cause bit errors and entire packets to be dropped. Combating fading has attracted substantial research efforts in the broader field of wireless communications. In contrast, in the specific context of MANETs, the issue has received relatively little attention, and is made more difficult by the lack of central coordination. Forward error correction and MAC-layer retransmissions [4] go some way towards combating channel unreliability. Some other types of approaches in the context of MANETs are link rate adaptation [11], transmission power control (e.g. [12]), and link reliability-aware routing [13]. Fading also results in a time-variant transmission range, albeit most MANET research assumes it is constant at the average value produced by the signal power fluctuations [13]. PHY

Due to the unreliable nature of the channel, lower-rate modulation schemes, which are more robust, must often be utilised. Either way, as previously stated, the wireless channel capacity is a critical resource, and fundamental capacity limits for omni-directional antenna-employing wireless networks have been established [ 14]. Numerous methods for overcoming such limits with directional antennas and multichannel MAC protocols have been investigated [ 8]. Elowever, throughput improvements achieved by such schemes typically come at the price of increased complexity, possible deafness to certain transmissions, difficulty in adapting to node mobility and incompatibility with the 802.11 MAC scheme [ 8].

2.2. MAC Layer Issues The 802.11 standard [4 ] specifies several channel access schemes, including the distributed coordination function (DCF) and enhanced distributed channel access (EDCA). Both of these are carrier-sensing multiple access with collision avoidance (CSMA/CA)-based schemes. The original DCF provided no support for QoSsensitive data. On the other hand, the EDCA scheme provides service differentiation through a plurality of channel access priority levels for different classes of data. Flowever, by definition, this provides only relative QoS. In fact, with contentionbased MAC schemes, like the DCF and EDCA, channel access is never guaranteed. Therefore, only average QoS, measured over a suitable period of time, can be guaranteed. Brief fluctuations in throughput, for example, must be tolerated. For further examples of MAC schemes which facilitate service differentiation, please consult [ 11 ], Many other MAC protocols for MANETs are surveyed in [ 5 ], [ 8]. Under the DCF and the EDCA scheme a device may only transmit when the channel is deemed idle. This means that neither the current device nor one of its carrier-sensing (cs) neighbours are transmitting or receiving. In fact, in MANETs since transmitters may be out of cs-range, a node may not know when all of it csneighbours are receiving and it may transmit. Thus, CSMA/CA-based MANETs are prone to collisions and the collision rate can be a dominant factor in the achievable QoS in near-saturated networks [ 15], [ 16].

The collision rate, and the fraction of time a node is able to gain channel access also affect nodes’ achievable throughput and their average packet servicing time. The latter in turn determines nodes’ queue sizes and hence has a major effect on end-to-end delay and delay jitter. Repeated collisions and buffer overflow due to inadequate channel access opportunities also contribute to the PLR. 2.3. Network Layer Issues Due to the CSMA/CA scheme, a node’s achievable level of channel access depends on the traffic load at cs-neighbours. Based on the conclusions above and in [ 15 ], it is therefore crucial to manage the network traffic load via admission control ( AC) if the 802.11 DCF and EDCA scheme are to be able to support QoS assurances. Most previous works on AC protocols have considered throughput to be the most important QoS metric [7 ]. Since, as was discussed above, the main metrics are related anyway, we focus our discussion on the problem of throughput assurance. Due to the nature of CSMA/CA-based protocols, as discussed above, AC protocol proposals of recent years (e.g. [ 17] ) typically employ the fraction of the time the channel is idle as an estimation of local residual capacity [7 ]. They have identified the need to factor mutual contention between cs-neighbours and all protocol overheads into the capacity requirement of a requesting session. Furthermore, they have identified mechanisms for determining whether a path’s cs-neighbours forwarding QoS-sensitive data have adequate capacity to accommodate the potential interference produced by a new session, as a prerequisite for that session to be admitted [ 17], [ 18], [ 19], [20 ]. Where data sessions of varying priority are concerned, lower priority sessions must not degrade the throughput of higher priority ones [21 ]. In order to discover those nodes, if any, that can adequately serve an applica-

tion, and

to avoid nodes with

networks rely on

inadequate resources, AC mechanisms for multi-hop

QoS-aware routing protocol [7 ]. Proposals for such protocols are highly numerous [ 5 ], [ 7]. Resource reservation, usually part of the AC or routing protocol, also plays an important role in QoS guarantees [7 ], while packet scheduling may be required specifically for meeting delay guarantees [ 5 ]. a

Node mobility poses two further problems to the provision of throughput assurFirstly, a transmitting node may move into another’s cs-range and reduce its available capacity. Secondly, route failures can create delays and lapses in throughput and cause packets to be dropped due to timeouts. Unexpected interference can be dealt with by reserving a portion of each node’s capacity for such events (e.g. as in [ 17], [ 19]). However, the capacity might never be used, and thus be wasted, or if ances.

too little is reserved, the scheme fails. Some works also suggest pausing or reducing the packet sending rates of sessions which are experiencing a degraded QoS [ 17], [ 19], [20 ]. Often this approach is also applied in the case of route failures. But what if session throughput requirements are not flexible? One intuitive solution is to have alternative routes ready at all times. Although dozens of proposals exist for multipath QoS-aware routing protocols, to the best of our knowledge, only a few, (e.g. [22 ], [23 ]), combine AC and multi-path routing for providing robust throughput guarantees in 802.11-based MANETs.

The proposal of [22] stores all full routes with sufficient capacity to the destination and uses one primary path for the requesting session. All alternative paths are capacity-tested periodically, ensuring that if the primary route fails, all stored paths have sufficient capacity to support the session. However, this method incurs periodic overhead. Also, the capacity of neighbours is tested by increasing the cs-range to hear possible sources of interference. This method is overhead-free but cannot reliably test the capacity of cs-neighbours outside of the transmission range. Also, a larger cs-range underestimates the residual capacity at cs-neighbours [16], [17]. Another protocol proposed in [23] is built upon an extension to DSR [24], which enables it to discover more routes by forwarding previously seen RReqs as long as they arrive from different neighbours. Each path’s capacity is estimated by utilising the delay between receiving probe packets. Traffic is split over at least two paths, adding robustness. However, since the probes inherently only test the path itself, it is not clear how it is ensured that the admission of new sessions would not introduce too much interference to cs-neighbours, or how inter-path interference is handled. Moreover, despite the importance of considering the increase in collision rate that a newly admitted session could cause, which can be concluded from the discussion in Section 2.2, and as discussed in [16], the previously mentioned works on admission control [17], [18], [19], [20], [23], neglected to do this.

3. Assured Throughput Service in the Face of Mobility Solutions Routing and Description Control Goals 3.1. Admission of

In this section we investigate the problem of throughput assurance in MANETs with different goals to the works mentioned above. We study the case where all traffic is QoS-sensitive and there are a much larger number of traffic sources and data sessions per source than in previous works [ 17], [ 18], [ 19], [20 ], [22 ]. Hence the AC and routing protocols are subjected to high levels of inter-path interference and highly dynamic QoS-related states. Furthermore, we assume that throughput requirements are inflexible and that all traffic is of equally high priority and therefore do not employ the service differentiation as in the EDCA scheme, rather the basic DCF. This focuses the evaluation purely on the performance of the network layer protocols in providing QoS assurances. Thirdly, for now we assume fixed- and lowrate links, as many of the previous works did [ 16], [ 17], [ 18], [ 19], [20 ], although unknown link capacities may be estimated by using the delay between transmitting probe packets of known sizes [25 ]. A final assumption is the lack of shadowing and fast-fading at the physical layer, as with all previously mentioned similar works [ 16], [ 17], [ 18], [ 19], [20 ], [23 ], since mechanisms beyond the scope of AC and routing are required to combat fading (Section 2.1).

In [16] we presented the design of the staggered admission control (StAC) protocol, and evaluated its performance in largely static scenarios together with our QoS-aware version of DSR [24]. With StAC, requesting throughput-sensitive

data sessions are initially subjected to a three-stage AC process described in [16]. In the first stage, routes with sufficient end-to-end capacity to the destination are sought. As in basic DSR [24], all discovered node-disjoint paths are stored. Then a route is selected, and its cs-neighbours are also tested (using limited flooding) for adequate capacity to admit the session (stage 2). Finally, in stage 3, the session’s packet sending rate is ramped up while the throughput is monitored, in order to test for increases in collision rates that would violate its throughput requirement. If, after a short time, the throughput is deemed adequate, the session is admitted. Node resource state update packets are used to maintain knowledge of the locally available capacities of each node on the paths used by a node. Therefore, when a route failure occurs, a session can be rerouted to the known route with the highest bottleneck capacity. However, this could introduce unacceptable interference to the new route’s cs-neighbours. Also, if no alternative routes were initially discovered, a temporary lapse in throughput could result, while one is discovered. Although this lapse could be short and acceptable to some applications, use of pre-tested backup routes could help avoid imposing unacceptable interference upon the interference to cs-neighbours and shorten the lapse even further. To be able to compare the two approaches, we propose an extension to StAC, called StAC-Backup, which pre-tests backup routes in a manner akin to [22 ], albeit with several key differences. Owing to a lack of space, only a brief overview of StACBackup’s main features is presented. Only one backup path per session is tested, and only when it is first selected, in order to reduce overhead. If no alternative route is known, a constrained route discovery is conducted. The route request (RReq) carries a copy of the primary route and each intermediate node only forwards the RReq if it is not part of the primary route. Once a suitable backup route is identified, its cs-neighbours are capacity-tested, as primary paths are in StAC [ 16]. Backup path test packets reserve capacity at intermediate nodes and their cs-neighbours (via limited flooding) to stop other sessions assuming use of that capacity along their backup paths. However, primary path tests initiated by new requests ignore these reservations, since the backup path might never be used. Nodes which are a part of, or are cs-neighbours of the backup path periodically test their remaining capacity. If it drops below 10%, signalling imminent congestion, a “backup path request rejected” message is sent to the session’s source which must seek another backup path. Note that the amount of capacity already consumed by the transmissions of the session’s packets on the primary route is known owing to the initial capacity test packets, and is added on to the capacity that would be available to the backup route if it had to carry the data session. Such testing continues while backup path reservations remain valid. Reservations are deleted if the backup path comes into use or another node is overheard rejecting it. This passive approach to backup route testing reduces overhead compared to the periodic sending of test packets. If a session’s primary route fails, the tested backup route becomes the primary route. If no suitable backup route has been identified, StAC-Backup reverts to StAC’s operation, described above.

In this section we describe the model used to evaluate the

performance of StAC 16 24 and described above. Classical DSR [ ] StAC-Backup, [ ], is evaluated as a benchmark. The popular ns-2 framework is employed for performance evaluation. One hundred nodes are initially distributed and move according to the steady-state random way-point mobility model (RWPMM) [26 ] in a 1660x 1660m simulated area. The node transmission and cs-ranges are assumed to be 250m and 500m respectively. These settings ensure that the average fraction of disconnected node pairs is below 5% and the average route length is greater than four hops, in order to rigorously evaluate the protocol. Node pause time between movements is 10s unless otherwise stated. Node speeds are selected according to a uniform distribution in the range {Vmin, Vmax} where Vmin is lm/s and the following values are used for Vmax: 2m/s (800s pause time), 2m/s (100s pause time), 2m/s (10s pause time), 4m/s, 8m/s, 16 m/s, 32 m/s, resulting in average node speeds of 0.62, 1.24, 1.42, 2.11, 3.24, 5.09 and 8.11 m/s

respectively. Sixty-seven of the

100 nodes

traffic sources, each with an offered load of 10 of 25kbps. Data packets are 512 bytes long. We initially assume a fixed transmission rate/channel capacity of 2Mbps. Simulations are run for 800s and session start times are uniformly distributed between 0 and 740s, since the common session duration is 60s.

constant bit-rate sessions with a

are

throughput requirement

A session is blocked if it does not pass the three-stage AC process described in Section 3.1 and in [16]. A session is dropped if the average throughput, monitored within a sliding window of 10s, drops below the session’s requirement by more than one packet size. On dropping, a notification is sent to the source, on any path, which aborts the session. A session is deemed completed if it is not dropped for 60 seconds. The results are not collected for the first and last 100s of simulation time. 3.3. Results and Discussion Some of our simulations results are presented in Figures 1-7. The metrics used are similar to those in [16]. Each data point is an average of 10 runs each with a different randomly-generated mobility and traffic scenario. As anticipated, and as becomes immediately clear from the figures, in most cases, the performance of all protocols deteriorates with increasing mobility according to all metrics, and even with proactive establishment of backup routes. As shown in Figure 1, and as expected, DSR admits the most sessions, since it employs no AC and all sessions are admitted as long as a route is established long enough to exchange session request (SREQ) and reply (SREP) messages between the source and the destination. However, as mobility increases, the increased route failure frequency, as well as congestion owing to the lack of AC mean that many SREQs and SREPs are lost, and the session admission ratio (SAR) decreases. StAC and StAC-Backup admit far fewer sessions since routes are capacity-tested and the throughput requirement

Figure 1. The fraction of requesting sessions admitted

Figure 2. The fraction of admitted sessions that were completed

Figure 3. The total network throughput minus the throughput promised to admitted sessions

Figure 4. The number of data packets dropped divided by the number transmitted

Figure 5. The average end-to-end delay experienced by successfully delivered data packets

Figure 6. The total network throughput

Figure 7. The transmission efficiency calculated as the total number of useful data bytes transmitted at the MAC layer divided by the total number of transmitted bytes. Control packets, packet headers and retransmissions after collisions do not count as useful transmitted bytes

must be upheld for a short time before a session is fully admitted [16]. However, StAC-Backup achieves a higher SAR since backup route establishment is triggered after stage 2 of admission control, meaning that more sessions successfully pass stage 3 in the face of route failures. On the other hand, Figure 2 shows that StAC-Backup achieves a lower session completion ratio (SCR) than StAC. At first this seems counter-intuitive, since pretested backup routes should be more reliable. However, note that the offered load was high (a total of 670 sessions offered throughout each simulation with a rate of 25kbps each) compared to the 2Mbps channel capacity and that the extra overhead incurred by backup route testing can cause congestion. In fact, the extra non-anticipated overhead being introduced into a highlyloaded network also explains why StAC-Backup consistently achieves a lower network throughput (Figure 6) and transmission efficiency (Figure 7) and a higher average packet delay (Figure 5) and frequency of throughput requirement violations (Figure 3) than StAC. For this reason we also studied a scenario with a much higher network capacity in order that the performance would be much less capacity-limited. In this scenario, we utilised 24Mbps as the node transmission rate, because this is the highest mandatory rate supported by the 802.11 standard [4]. Note that the actual network capacity does not increase 12-fold, because the slot times and inter-frame spaces, which determine transmission deferring and back-off times, may be the same in higher-rate PHYs as in lower-rate ones [4], as we have assumed here. This means that load-handling still plays a part in the performance. Table 2 shows that not only is StAC-Backup again able to achieve a higher SAR than StAC, but despite this, a higher SCR as well. Even at a maximum node speed of 32m/s, an average of 83% of sessions were completed using StAC-Backup, as opposed to 65% and 43% by StAC and DSR respectively. Due to its lack of AC, DSR was still outperformed by StAC in terms of providing QoS assurances. However, the results for both scenarios

Table 2. Simulation results employing the model of Section 3.2, except that maximum node speed 32m/s and the channel capacity 24Mbps. Each result is an average of 10 runs with different randomly-generated mobility and traffic =

=

scenarios. Abbreviations: SAR Session admission ratio, SCR tion ratio, T/p throughput, APD average packet delay, PLR =

=

= —

NTE

= *=

normalised transmission

efficiency (see Figure Net. t/p

session complepacket loss ratio,

=

=

7 for the definition)

-

Protocol

SAR

SCR

Network T/p

promised t/p

APD

PLR

NTE

DSR StAC

59%

43%

0.10

0.62

65%

-614kbps -139kbps -91kbps

0.049

38% 44%

823kbps 668kbps 713kbps

0.077 0.12

0.074 0.041

0.55 0.47

StAC-

83%

Backup show DSR is able to achieve a higher overall network throughput since it admits so many more sessions, albeit this degrades the QoS of individual sessions. This implies that StAC and StAC-Backup not only lower the ratio of useful transmitted bytes (Figure 7 and Table 2), but also the capacity utilisation of the network through overly-careful AC. In some cases, increased mobility also seems to improve the performance of DSR (Figure 3 and Figure 5), but this is misleading in terms of providing QoS assurances. With increased mobility, the PLR increases substantially (Figure 4), but the SCR does not decrease proportionately (Figure 2), showing that a small number of sessions are affected adversely. When those are dropped, the remaining sessions suffer less congestion and enjoy lower average delay.

4. Conclusions and Future Directions This article first discussed how various issues at the PHY, MAC and network layers affect the QoS that can be provided by a MANET. In particular, an assured throughput service was investigated with the aid of a proposed routing and admission control (AC) protocol. Two approaches to adding robustness against route failures were compared: that of relying only on routes discovered by the initial flooding-based route discovery, and that of pro-actively discovering a backup route for each admitted session and ensuring that it and its carrier-sensing neighbours could accommodate the session if it was rerouted. Simulation results showed that it is worth pre-testing backup routes only if the incurred overhead is anticipated and sufficient capacity is available or reserved to accommodate it. In this case, a combination of AC and knowledge of pre-tested backup routes can ensure that the vast majority of sessions maintain their desired throughput even with high mobility and route failure rates. Otherwise, the extra overhead incurred can be counterproductive, causing QoS assurance violations. An adaptive approach, which adjusts the frequency and likelihood of backup route discovery and testing according to

the residual capacity and the level of mobility, is likely to perform better than the two static-rule-based approaches investigated. As suggested both by our conclusions and the works of others [15], [22], combined multi-path QoS-aware routing and AC is a promising approach for the provision of robust QoS assurances in MANETs. Alternative paths between a node pair can be used as a contingency, used for traffic splitting for added robustness, or employed for sending redundant packets to be used in error-recovery. Future work to compare such approaches would be useful. Moreover, many previous solutions have been tested using only a small number of data sessions. This work has attempted to address this issue, but it has been highlighted that overly-careful AC, while improving the QoS of admitted traffic, can easily under-utilise the network resources. Future work to bring performance closer to optimal utilisation is required. Further work on interference- and collision-aware methods to deal with traffic with multiple QoS constraints, with varying priorities and with variable link capacities in large mobile networks would also be useful. A full system for providing QoS assurances in MANETs is inherently crosslayer and requires mechanisms at the PHY, MAC, network and possibly transport layers. Many works consider combined MAC and network layer solutions but ignore the PHY layer. Techniques to combat fading, for example, should be integrated with higher-layer methods in order to be able to evaluate QoS-assurance solutions in more realistic simulation environments.

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Adaptive Cell Sizing Scheme for Asymmetric Traffic Accommodation in CDMA/FDD Cellular Packet Systems Kazuo Mori1 Mie University, Tsu, Japan Abstract. The accommodation of asymmetric traffic between uplink and downlink is essential to realize efficient multimedia mobile communication systems. This chapter discusses asymmetric traffic accommodation in CDMA/FDD cellular systems and proposes its efficient scheme using an adaptive cell sizing technique. In the proposed scheme, each base station autonomously controls its coverage area so that almost the same quality can be provided across the service area under the asymmetric traffic conditions. The numerical results show that, under asymmetric traffic conditions, the proposed scheme can provide fair communication quality across the service area in both links and can improve total transmission capacity in the uplink. Keywords: Asymmetric traffic, Frequency division duplexing, Cellular system, CDMA, Multimedia communications, Cell size control.

1. Introduction Mobile communication systems have recently provided many kinds of services and have carried multimedia traffic such as data and video traffic in addition to traditional voice traffic. The properties of the traffic over the recent mobile communication systems have been changing because of providing these new services. Current cellular communication systems have a symmetric structure whose uplink (mobile to base station) and downlink (base to mobile station) occupy the same bandwidth because the symmetric structure is suitable for the traditional voice traffic, which exhibits symmetric property in the traffic between the uplink and downlink. However, the traffic in multimedia services is generally asymmetric between uplink and downlink. In World Wide Web (WWW) access, for example, a large amount of traffic is conveyed in the downlink, while small amount is in the uplink. Moreover, the degree of this asymmetry would vary temporally and with geographical locations. This asymmetry would waste the radio resource and degrade its utilization in the systems with symmetric radio resource allocation. In addition, the traffic asymmetry causes geographical non-uniformity of the communication quality across the service area and also brings the overall performance degradation in the cellular communication systems. Then, many approaches have therefore been investigated to accommodate asymmetric traffic in mobile communication systems [ 1 ]—[ 9]. 1 Corresponding Author: Kazuo Mori, 1577 Kurimamachiya-cho, Tsu, MIE, 514-8507, Japan. [email protected]

DOI: 10.1201/9781003336853-6

Adaptive Cell Sizing Scheme

Time division duplexing (TDD) scheme has the capability of allocating radio resources (time slots) to uplink or downlink according to the dynamics of traffic balance between links. Then the shared-TDD scheme [10] has been proposed for accommodating asymmetric traffic, and its applications to CDMA cellular systems have been investigated [2]—[9]. In the shared-TDD scheme, however, inter-link interference, which the uplink/downlink signals interfere with downlink/uplink signals between the adjacent cells, fundamentally appears due to autonomous resource allocation to each link by every base station. This interference causes degradation in the system performance [4]. In frequency division duplexing (FDD) cellular systems, on the other hand, the autonomous radio resource allocation according to the traffic balance within a cell is impossible because the radio resource allocated to each link is fixed and this allocation cannot be changed arbitrarily by base stations. Therefore, an efficient asymmetric traffic accommodation is a challenging issue in FDD cellular systems. However, there are few researches performed for cellular systems with the FDD scheme. The current major commercial cellular systems, for example GSM, PDC and W-CDMA systems, employ the FDD scheme, and therefore, it is really important to achieve efficient asymmetric traffic accommodation in FDD based cellular systems. By the way, the adaptive cell sizing and shaping techniques [ 11 ]—[ 13] have been proposed as one of countermeasures against the performance degradation due to the geographical non-uniform traffic distributions. In this technique, each base station autonomously adjusts its coverage area by controlling its pilot signal transmission power or its antenna beam forming so that the traffic load managed by each base station becomes uniform across all base stations. This technique is considered to be useful for the asymmetric traffic accommodation in FDD cellular systems. Because the degree of the asymmetry is generally non-uniform between cells, the efficient asymmetric traffic accommodation can be realized by flexible adjustment of the traffic volume between cells by using the cell sizing, even when the system has the fixed radio resources allocated to both links. This chapter discusses asymmetric traffic accommodation in CDMA/FDD cellular packet systems and proposes its efficient scheme using the adaptive cell sizing technique. In the proposed scheme, every base station autonomously controls its coverage area so that almost the same communication quality can be achieved across the service area under asymmetric traffic conditions. The control of the coverage area is carried out independently for the uplink and the downlink. The proposed scheme is evaluated by computer simulation to demonstrate the effectiveness of the proposed scheme.

2. Adaptive Cell Sizing Technique The adaptive cell sizing (ACS) technique keeps the communication quality uniform in CDMA cellular systems with geographical non-uniform traffic distribution [ 11 ]. The uniform quality across the service area is provided by autonomously controlling

3. Asymmetric traffic accommodation using adaptive cell sizing the pilot signal transmission power Pplt and the target transmission power control (TPC) at each base station.

reception

powerPtg

In the ACS control, each base station monitors the communication quality in its own cell and compares it with a fixed target value, which is set beforehand [11]. As the monitored quality, for example, the packet reception success rate is used in [11]. After the comparison, the base station decreases Pplt to reduce its cell size when the monitored quality is below the target. As a result, the mobile stations near the cell boundary make a handover to other base station and the traffic volume decreases in the cell, and thus, the communication quality improves. In contrast, when the quality is greater than the target, the base station increases Pplt to expand its cell size. Since the handover stations tend to exist far from the new base station, the communications with these mobile stations require a large transmission power and this causes large interference to the adjacent cells. Hence, to overcome this interference, the base station changing its Pplt also adjusts its Ptg for TPC. As described in [11], the Ptg(i) is controlled as following equation:

Ptg

=

Ptg(i)' .Pplt(i)' /Pplt(i) (1)

where Ptg(i) and Ptg(i)' are the target reception power for the i-th base station after and before the ACS control, and Pplt(i) and Pplt(i)'are their pilot signal transmission power after and before the control, respectively.

3. Asymmetric traffic accommodation using adaptive cell sizing The asymmetric traffic can be interpreted as a sort of geographical non-uniform traffic distributions between cells. Therefore, the ACS technique is considered to be useful for the accommodation of asymmetric traffic in CDMA/FDD cellular communication systems. The proposed scheme introduces a modified ACS control, which is enhanced from the scheme described in [11], individually into uplink and downlink. In the proposed scheme, the cell size associated with each link is independently controlled at each base station, as illustrated in Figure 1.

Figure 1. ACS for asymmetric traffic accommodation

The proposed scheme has a new control mechanism for the cell size control because the control by adjusting the pilot signal transmission power Pplt is difficult to realize independent control of the cell size in each link. Hence, in the proposed scheme, the Pplt is constant for all base stations in the service area, which is different from the conventional ACS control, and the cell size is controlled by using cell size information. 3.1. Cell size information The cell size information is broadcast form the base stations to their mobile stations via the pilot channel (signal) with constant transmission power of Pplt. The cell size information includes uplink cell size information Isl—u,downlink cell size information Isl—d, and uplink target reception power Ptg—u, and they are utilized in a cell selection phase at each mobile station. The uplink and downlink cell size information Isl—u and Isl—d are important parameters which determine the cell size in the proposed scheme. They are controlled so as to take a small value under heavy traffic load conditions and a large value under light load conditions. The mobile stations decide the serving base station, which they communicate with, by using the cell size information. 3.2. Selection of serving base station The mobile stations estimate the short-term average propagation loss Pls(i) from the i-th base station by using the pilot signal transmitted with same power from all base stations. And then, they calculate cell selection values for the i-th base station: Psl—u(i) for the uplink and Psl—d(i) for the downlink. The Psl—u(i) is calculated by using the estimated Pls(i) and Isl—u(i) received from the i-th base station: Psl—u(i)

=

Isl—u(i)/Pls(i) (2)

Equally, the downlink cell selection value Psl—d(i) is also calculated by the Pls(i) and the received Isl−d(i). The mobile stations select the base station ju which gives the largest Psl—u(i) as the serving base station for the uplink. Equally, the base station jd having the largest Psl—d(i) is selected for the downlink: ju = arg max Psl—u(i), (3) i

jd = arg max Psl—d(i). (4) i

After these selections, mobile stations transmit/receive the packet to/from the serving base stations. In the uplink and downlink communications, the target reception power Ptg—u(ju) and Ptg—d(jd) are used in the calculation of the transmission power in TPC, respectively.

In the proposed scheme, the serving base station ju for the uplink is not always the same as the serving one jd for the downlink because Isl—u(i) and Isl—d(i) are not identical due to the ACS control, and thus, the cell size (or cell coverage area) generally differs between the uplink and the downlink, like Figure 1. Although this would bring additional system cost, for example in handover procedure, the aim in this chapter is to achieve efficient radio resource utilization, which is the most important issue in mobile communication systems, and the impact of mobile station having different serving base stations to the system cost will be discussed in the future work. 3.3. Cell size control The base stations control the uplink and downlink cell size information Isl—u and Isl—d to adjust their cell size. The Isl—u and Isl—d of each cell are initially set to same values, which mean the cell size is almost the same for all cells, and are controlled to adequate values according to the traffic conditions. In the proposed scheme, they are controlled based on the packet reception success rate, which is defined as the ratio of the number of successful reception packets at the destinations to that of transmitted packets. The packet reception success rate psuc takes a large value as the traffic load is small, whereas psuc is small for heavy traffic loads. Hence, when psuc is a large value, the base station increases Isl to spread its coverage area and to accommodate more traffic. In contrary, in the case of a small psuc, the base station has to straiten its coverage area to maintain the quality of the communications, and then Isl is decreased to a smaller value. Each base station measures the packet reception success rate psuc—u in the uplink and psuc—d in the downlink for an observation period Tob [slots]. Based on the measured uplink packet reception success rate psuc—u, each base station controls the uplink cell size information Isl—u(n) at time n by using the following equation: up er I Subscript s l minus u Baseline left-parenthesi n right-parenthesi equals StartLayout 1st Row 1st Column StartLayout Enlarged left-brace 1st Row up er I Subscript s l minus u Baseline left-parenthesi n minus 1 right-parenthesi semicol n 2nd Row up er I Subscript s l minus u Baseline left-parenthesi n minus 1 right-parenthesi dot normal up er Delta up er I Subscript s l minus u Baseline semicol n EndLayout EndLayout StartLayout 1st Row StartAbsoluteValue p Subscript s u c minus u Baseline minus up er T h Superscript u Baseline EndAbsoluteValue les -than-or-equal-to normal up er Delta times up er T h Subscript u p d minus u Baseline slash 2 times normal a normal n ormal d times p Subscript s u c minus u Baseline not-equals 1 2nd Row normal o normal t normal h normal e normal r normal w normal i normal s normal e com a EndLayout

(5) where

—u a target value for the packet reception success Thu, ΔThupd—uand ΔIslare is introduced rate, a control margin and a control step for Isl—u. The target value Thu to maintain the channel quality constant for all cells and adaptively set to adequate values according to the current traffic load as described in Sec.3.4. The control margin ΔThupd—u is introduced to avoid unnecessary control due to the variation in the measured Psuc—u caused by the traffic fluctuation in a quite short term. The control step is controlled so as to be a large value when the difference between measured psuc—u and Thu is large and a small value otherwise to cope with the traffic fluctuations rapidly. The ΔIsl—uis given by:

ΔIsl—u

=

C

•

psuc—u

Thu.(6)

In the above equation, C is an updating constant with a positive value. Equally, the downlink cell size information Isl—d is controlled based on the measured downlink packet reception success rate psuc—d by using Eqs.(5) and (6). After then, each base station updates the target reception power Ptg—u and Ptg—d at time n by using the following equation to maintain the balance of the interference power between the cells: Ptg(n)

=

Ptg(n

—

1). Isl(n —

1 )/Isl(n).(7)

These updates are carried out every observation period Tob [slots]. 3.4. Setting of target packet reception success rate The target values for packet reception success rates are fixed in the conventional scheme (for example [11]). However, the control with the fixed target values cannot cope with fluctuations of the degree of traffic asymmetry and the traffic load. In the proposed scheme, the target values Thu and Thd are autonomously in to values order to with the traffic fluctuations. Base staupdated adequate cope tion controllers (BSC) collect the packet reception success rate for each link from all of the base stations under their control and calculate the average values psuc—av—u for the uplink and Psuc—av—d for the downlink, averaged the collected packet reception success rates. Then, they inform psuc—av—u and psuc—av—d to their base stations and the base stations set the target values Thu and Thd at psuc—av—u and psuc—av—d informed from the BSC. This updating control of the target values is not carried out if all of psuc—u ± ΔThhlt or psuc—d collected by the BSC are in the range of psuc—av—u or Psuc—av—d ± ΔThhlt, where ΔThglt is a control margin for the and Thd controls. The ΔThhlt is used to avoid unnecessary control due to the variation in the psuc caused by the quite short-term traffic fluctuations. Therefore the system needs to set the ΔThhlt at a little larger value than the deviation in the psuc under the static traffic conditions and we can apply the same value to the both links. Thu

According to the above controls, the system would keep the traffic load within each cell (coverage area) almost constant in the service area, and communication quality would be also maintained almost constant for all cells, under asymmetric traffic conditions.

4. Simulation Model To evaluate the performance of the proposed scheme, we have carried out computer simulations assuming the following conditions: – The service area consists of 19 cells, as illustrated in Figure 2. All base stations are under the control of one base station controller (BSC). – Mobile stations are uniformly distributed across the cells.

Figure 2. Cell model

– The multiple access protocol for the uplink is CDMA slotted ALOHA. The downlink also has a slot structure. Slot synchronization is perfect among all cells. – Each packet employs a unique spreading sequence so that the sequences used by arriving packets do not collide. – Transmission power is controlled so that the reception power at the destination becomes the target reception power Ptg—u for the uplink and Ptg—d for the downlink. TPC is perfect without errors. 4.1. DS/CDMA Channel Model Each radio channel suffers distance attenuation with a coefficient α and shadowing fluctuation that has a log-normal distribution with a standard deviation of σsh [dB]. Let Ptx be the transmission power; then the received power Prx at the receiver can be expressed as =Ptx · 10s/10 ·

(8) d-α,

Prx

=

Ptx/Pls

where Pls is propagation loss, S is the shadowing fluctuation in the path from the transmitter to the receiver, and d is the distance between them. In the CDMA system, packets interfere with other packets arriving from within the service area. Thus, the uplink SIR SIRu (i) and the downlink SIR SIRd(i) of the desired packet i can be calculated as up er S up er I up er R Subscript u Baseline left-parenthesi i rght-parenthesi equals up er P up er G dot up er P Subscript r x Baseline left-parenthesi i rght-parenthesi slash normal up er Sigma UnderUnderscript k equals 1 Underscript k not-equals i Endscripts Overscript k Subscript u Baseline Endscripts up er P Subscript r x Baseline left-parenthesi k right-parenthesi com a

(9)

up erSup erIup erRSubscriptdBaselineleft-parenthesi irght-parenthesi equalsup erPup erGdotup erPSubscriptrxBaselineleft-parenthesi irght-parenthesi slashleft-parenthesi up erFitalic0normalup erSigmaUnderUnderscriptkequals1Underscriptknot-equalsiEndscriptsOverscriptkSubscriptdiBaselineEndscriptsup erPSubscriptrxBaselineleft-parenthesi kright-parenthesi plusnormalup erSigmaUnderUnderscriptkequals1Underscriptknot-equalsiEndscriptsOverscriptup erKSubscriptdeBaselineEndscriptsup erPSubscriptrxBaselineleft-parenthesi kright-parenthesi right-parenthesi com a

10)

where Prx(x) is the received power of the packet x, calculated by Eq.(8), PG is processing gain, Ku is the number of arriving uplink packets at the base station, Kdi is the number of downlink packets arriving from the same base station at the mobile station, and Kde is the number of downlink packets arriving from other base

stations. F0 is an orthogonality factor defined as the fraction of total received power that will be experienced as intra-cell interference due to multi-path propagation [ 14].

The transmission power is assumed to be constant for the duration of a packet, that is, the SIR is constant for packet duration. In this chapter, we assume the receivers can receive the packet which satisfies the required SIR [15]. 4.2. Traffic Model To simulate asymmetric traffic condition in each cell, we introduce an asymmetry ratio Rasym which gives the ratio of the traffic load of the downlink to that of the uplink within a cell. The asymmetry ratio Rasym is independently given for each cell. The total traffic load Gto, which is the sum of uplink traffic Gup and downlink traffic Gdn, is assumed to be the same for all cells, where the traffic load Gto, Gup, and Gdn are defined as the average number of generated packets during a slot duration. Rasym. Hence, Gup and Gdn for each cell can be obtained by Gto and Mobile stations arrive following a Poisson arrival with an average of Gup for uplink and Gdn for downlink in each cell. One packet is generated for each mobile station. Each station re-transmits the packet which the destination fails to receive successfully. The re-transmission intervals follow an exponential distribution with an average of Tnx. The maximum number of re-transmissions is Nrtx for each packet.

5. Performance Evaluations 5.1. Parameter settings and evaluated performances In the

simulations,

we

used the parameters listed in Table 1. We have evaluated the

packet reception success rate psuc for each cell and an average packet dropping rate Pdrop, averaged over all cells. The packet dropping rate pdrom is defined as the ratio of the number of unsuccessfully received packets at the destinations to the number of generated packets at the sources. These performances for the proposed scheme have been compared with those without any ACS controls (“w/o any controls” in Figures) and those for the ACS control with the fixed target packet reception success rate (“fixed ACS” in Figures and hereafter called “fixed ACS control”). We assume four static traffic conditions, where the asymmetry ratio Rasym in each cell is given beforehand as shown in Table 2 and does not vary in time. The total traffic load Gto is a parameter in the evaluations. 5.2. Packet reception success rate Figure 3 shows the packet reception success rate psuc for the proposed scheme and without any controls as a function of maximum asymmetric ratio Rasym—max in the case of the total traffic load Gto = 3.0. Figure 3(a) and 3(b) show the psuc in the uplink and the downlink for cell 0, 2, 3, and 10, as indicated in Figure 2. The psuc without any controls varies between cells in the both links due to the different

Table 1. 1. Simulation Simulation parameters Table

Cell radius Distance attenuation coefficient Standard deviation of shadowing

77;

Reel!

500 3.5 7 16

®sh

PG

Re-transmission interval Maximum number of re-transmissions Slot duration Observation period Control margin for Isi update

margin for Updating constant

Value

a

Processing gain Orthogonality factor Required SIR

Control

Symbol

F0 SIR,

0.6

Trtx Nnx

10 3

Tslot Fob

0.001 1000

Initial target reception power Range of target reception power

Pfg

a

i

n t

[S]

[slots]

0.025 1 20

C 1st

[dBj [slots]

0.05

*

AThhit

Initial cell size information Range of cell size information 7s/_„, /j_r;

[dBJ

5

Afhupd^ji

update

[m]

Isl—d

0.0 to 40.0 0 ~20 to 20

Rfg—d

Ptg-U, Ptg-d

[dBj [dB] [dB] [dB]

in each 2. Asymmetric traffic conditions: conditions: Rasym each cell cell Table 2. Asymmetric traffic Table Gd„/Gup) in Rasy,n (= Gdn/Gup) Cell number 0

1

2

3

4

5

6

Pattern A B

C D

0.82 0.54 0.33 0.18

0.82 0.82 0.82 0.82

1.22 1.86 3.00 5.67

1.22 1.22 1.22 1.22

0.90 0.67 0.54 0.43

1.00 1.00 1.00 1.00

1.11 1.50 1.86 2.33

8_18 odd

even

1.11 1.50 1.86 2.33

0.90 0.67 0.54 0.43

R, 1.22 1.86 3.00 5.67

asymmetry ratio Rasym between cells. Especially, the difference in psuc between cells becomes large in the both links under the condition with a large Rasym—max. Applying the proposed scheme, however, psuc has no difference between cells in the both links. Moreover, the proposed scheme can maintains almost the same psuc performance in the both links regardless of the maximum asymmetric ratio Rasym—max. Therefore, the proposed scheme can achieve the same communication quality for all cells regardless of the degree of traffic asymmetry. Figure 4 shows the packet reception success rate psuc for the proposed scheme and the fixed ACS control as a function of Gto in the case of the maximum

Figure 3. Packet reception success rate psuc as a function of Rasym—max

Figure 4. Packet reception success rate psuc as a function of total traffic load Gto

asymmetric ratio Rasym—max = 3.0. In the fixed ACS control, the variance in psuc between cells become small for both links in comparison with the case without any controls (see Figure 3). However, the fixed ACS control cannot achieve the same psuc for all cells under all traffic load conditions. This is because a suitable Thu and Thd exist at each traffic load for this ACS control. In the proposed scheme, psuc has no difference between cells in the both links for all traffic conditions because the suitable Thu and Thd are automatically fed into the ACS control. Therefore, the proposed scheme can achieve the same communication quality for all cells regardless of the traffic load under asymmetric traffic conditions. 5.3. Packet dropping rate Figure 5 shows the packet dropping rate pdrop for the proposed scheme, for the fixed ACS control and without any controls as a function of Gto in the case of Rasym—max = 3.0.

For the uplink performance, the pdrop degrades for the fixed ACS control and without any controls as the total traffic load Gto becomes large. However, although pdrop for the proposed scheme also degrades for a large Gto, the proposed scheme obtains better pdrop performance for all traffic load conditions than other schemes. Hence, the proposed scheme has the superior pdrop performance to other schemes and can increase system capacity under asymmetric traffic conditions in the uplink.

Figure 5. Packet dropping rate pdrop as a function of total traffic load Gto

For the downlink, pdrop performance has no difference between three schemes and thus the proposed scheme cannot achieve the capacity improvement in the downlink. This is because the downlink channel is a point to multi-point channel and has no drastic performance degradation at the traffic region over its channel capacity, as observed in the uplink channel (this channel is a multi-point to point channel). Due to this channel characteristic, the performance improvement cannot be always obtained for all cells, and therefore there is no change in the pdrop performance averaged over all cells.

6. Conclusions This chapter has discussed the asymmetric traffic accommodation in CDMA/FDD cellular packet systems. The asymmetric traffic accommodation scheme using the ACS control has been proposed to enhance the system performance. The packet reception success rate and packet dropping rate have been evaluated by computer simulation. The simulation results show that (1) the packet reception success rate is the same for all cells under the various degree of traffic asymmetry and the various offered traffic loads in the uplink and the downlink, (2) the packet dropping rate is improved only in the uplink. These results show that the proposed scheme can achieve the same communication quality across the service area in both links and improve the system capacity in the uplink under the asymmetric traffic conditions. Therefore, the proposed scheme is effective for the accommodation of asymmetric traffic in CDMA/FDD cellular packet communication systems.

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A Dynamically Self-organized Clustering Protocol for Mobile Ad Hoc Networks Chung-Hsien Hsu and Kai-Ten Feng1 Department of Communication Engineering National Chiao Tung University, Hsinchu, Taiwan Abstract. In recent years, various types of ad hoc routing protocols have been studied in the mobile ad hoc networks. Specifically, the cluster-based hierarchical routing algorithms have been developed to increase the system performance. The control packets can be reduced in the cluster-based schemes due to the decreased numbers of mobile node that join the routing

processes. However, the significant overhead resulting from the formation of the cluster structure

make it

unsatisfactory

to

assist the

design

of routing

algorithms, especially

with small

number of communication pairs in the network. In this article, a dynamic clustering protocol is developed in order to alleviate the excessive overhead induced from conventional cluster formation. The cluster structure is simultaneously established along with the construction of the on-demand routing path. Depending on the existing number of communication pair within the network, the clusters are adaptively formed, maintained, and disbanded. The effectiveness of the proposed clustering algorithm is observed via the simulation results. The proposed scheme outperforms the existing cluster-based and non-cluster-based routing protocols under different numbers of communication pairs within the network.

Keywords: On-demand routing, clustering structure, mobile ad hoc networks.

1. Introduction A mobile ad hoc network

(MANET) consists of wireless mobile nodes that coopercommunicate with each other without the existence of fixed network infrasatively tructure. Depending on different geographical topologies, the mobile nodes are dynamically located and continuously changing their positions. It becomes important to design efficient and reliable multi-hop routing protocols to discover, organize, and maintain the routes in MANETs. Different types of ad hoc routing protocols have been developed in recent years. the underlying structures, the ad hoc routing algorithms can be classified into three categories: the flat routing, the geographic position-assisted routing, and the hierarchical routing [ 1 ]. The design and operations of the ad hoc routing protocols are affected by the different types of structures. The flat architecture is adopted in the flat routing approaches (e.g., DSDV [2 ], AODV [3 ], and DSR |4|). where each node equally participates in packet delivering and forwarding. With the

According to

location information of the mobile nodes, the geographic position-assisted routing schemes (e.g., LAR [ 5 ], VAR [ 6], and PMLAR |7[) can reduce the routing overhead by restricting the region for packet forwarding. 1 Corresponding Author: Kai-Ten Fengis with the Department of Communication Engineering, National Chiao Tung University, Hsinchu, Taiwan (e-mail: [email protected]).

DOI: 10.1201/9781003336853-7

A Dynamically Self-organized Clustering Protocol The hierarchical

routing algorithms (e.g., CGSR [ 8] and COB [9 ]) construct hierarchy by grouping the nodes into explicit clusters. A leading node (i.e., the clusterhead) on behalf of the cluster is responsible for communicating with other clusters in the network. The routing tables and the control overhead can therefore be reduced in the cluster structure since only a fraction of nodes are required to join the routing processes. However, the cluster formation is a prerequisite in order to conduct multi-hop routing within MANETs. Several cluster formation algorithms are proposed as in [ 10 ] [ 14 ]. The lowest-identification (LID) scheme [ 10] selects the node with the lowest-ID as the clusterhead, which provides an efficient and low-cost clustering process. The LID with adaptive ID reassignment algorithm [ 11 ] further extends the LID scheme with the mechanism for cluster maintenance. The highest degree method [ 12] utilizes the node's location information for cluster formation; while the node with the largest number of neighbors is selected as the clusterhead. The weighted clustering algorithm and the weight-based adaptive clustering algorithm [ 14] choose their clusterheads by considering the weighting among various factors, e.g., mobility, degree, and battery power. The benefits of using the cluster structure are investigated as in [ 15 ]. Obviously there are significant costs associated with the cluster structure, including the construction of the clusters, the exchanges of cluster-related control messages, and the ripple effect [16] for re-clustering the structure. It will be beneficial to construct the clusters on-demand based on the current requirement and the existed resources. In this article, an on-demand routing-based clustering (ORC) protocol is proposed. The ORC protocol modifies the route request/reply processes from conventional on-demand routing algorithm (e.g., the AODV protocol) to construct the cluster structure. After the route discovery process has been completed, the clusters are automatically established along the constructed route. The cluster structure will be utilized in the remaining processes for packet delivery. The advantage of using the ORC protocol is that the cluster-based multi-hop routing becomes available without extra costs that are induced by the formation of clusters. The effectiveness of the proposed ORC algorithm is validated via simulation. The rest of this article is organized as follows. Section 2 states the network model and the problem statement. The proposed ORC protocol is described in Section 3. The performance evaluation of the ORC algorithm is conducted in Section IV. -

Section V draws the conclusions.

2. Network Model and Problem Statement 2.1. Network Model Any signal transmitted over

a wireless medium experiences the attenuation and the interference effects. The received signal power varies in proportion to d–α, where d is the distance between the transmitter and the receiver. The exponent α characterizes the communication medium, whose value typically falls between 2 and 4. Based on this model, it is assumed that each node can calculate the distance between

2. Network Model and Problem Statement

Figure 1. The schematic diagram of an exemplified network topology of the proposed ORC protocol the

packet transmitter and itself according to the received signal strength of the packet. Moreover, each node can overhear the packets that are transmitted within its receiving range. It is also noted that each node is assigned with a unique id, however, is considered location-unaware, i.e., does not equipped with the positioning system. A MANET can be modeled as an undirected graph as G (VG, EG), where two nodes {nu,nv} ∈ VG are connected by an edge (nu,nv) ∈ EG if they can communicate with each other. The routing path Ps,d V from the source node ns to its corresponding destination node nd is a sub-graph of G. The edge if and only if two nodes {ni, nj} ∈ V and |hops(ni)—hops(nj)| 1, (ni, nj) ∈ E where hops (ni) represents the number of hops between the source node ns and node A ni. cluster is denoted as Cx, which contains arbitrary number of nodes within MANET, i.e., V Considering node nx ∈ VCx as the clusterhead of Cx, the set of nodes nu ∈ V are denoted as the cluster members of Cx if and only if nu, ∈ EG. The cluster gateways are defined if one of the following conditions is nx) n satisfied: (1) node np is called the cluster gateway of Cx and Cy if np ∈ ( ); (2) nodes npand nq are cluster gateways if (np,nq)∈ EG where np ∈ v and with Cx∉ Cy. Moreover, the neighboring set V VG of a cluster Cx nq ∈ V is represented as a collection of nodes nv ∈ V if and only if nodes nu ∈ V and (nu, nv) ∈ EG. An exemplified network topology is shown in Figure 1. Considering the cluster C2 node n2is the corresponding clusterhead with its transmission range =

=

=

.

indicated as the solid circle. Nodes n6 to n13 are the cluster members of C2, where nodes n6, n7, and n8 are served as the cluster gateways between C2 and other clusters. Moreover, node n15 ∈ V since n15∈ V but is connected with node n8∉V .

2.2. Problem Statement The concept of the proposed ORC algorithm is to design a distributed, local, and scalable protocol that constructs the cluster structure on-demand for the MANET. The clusters are constructed while a source node intends to communicate with its corresponding destination node. In other words, the routing path and the cluster structure are constructed simultaneously, which results in the construction of the cluster structure only along the routing path instead of the entire network. The following three conditions are required to be satisfied for the constructed cluster structure: 1. Partial participation condition. A cluster structure Ss,d, which constructed simultaneously with a routing path Ps,d can be modeled as Ss,d = (V

) ⊆ G. The vertex set V

)},

where node nx is the clusterhead of the cluster Cx. The edge (nu, nv) ∈ E if and only if two nodes {nu, nv}∈ V and (nu, nv) ∈ EG. The partial participation condition indicates that only the nodes associated with the construction of the on-demand routing are required to join the cluster structure. 2. Connectivity condition. This condition states that there exists a path Px,y ⊆ Ps,d which connects two clusters Cx and Cv in a cluster structure Ss,d.For all nodes ni ∈ V are required to either be the clusterhead or the cluster gateway. 3. Localized stabilization condition. The node nu ∈ V can be shut down or moved out of its original cluster Cx; while a new node nv ∉ V may move into the cluster Cx. This condition indicates that the proposed ORC protocol should recover these situations in a localized manner such that both the connectivity and the partial participation conditions are satisfied.

3. The Proposed On-demand Routing-based Clustering Protocol In this section, the proposed ORC algorithm is presented. The main objective of the ORC protocol is to simultaneously construct the routing path and the cluster structure. Figure 1 illustrates the schematic diagram of an exemplified network topology of the ORC algorithm, where node n4 is the source node and node n5 is the corresponding destination node. In the proposed ORC protocol, two parameters are considered for constructing the cluster structure: the number of nodes in the density area and the hop factor. The density area Ai is defined as a circular region centered at the corresponding node ni The set of nodes located within the density along the constructed path, i.e., ni ∈ V .

of node ni can be obtained as V ∈ EG, dji ≤ rd, ∀j}, {nj ∈ VG | (njni,) where djiis defined as the distance between nodes nj and ni.rd is the pre-determined radius of the density area for all the nodes within the network. The number of nodes 2 for node located in node ni's density area is represented as| V (e.g., | V| area

=

=

|

in Figure 1 ) which indicates the number of backup nodes for node ni. The hopc(ni) ni in factor is also defined for each node a which hop routing path Ps,d, ∈V and the nearest represents the number of hops between the current node ni clusterhead nx ∈ V under the condition that hops(nx)— hops(ni) ≥0. It is noticed that the condition indicates that the nearest clusterhead is always selected from the “downstream” of the path. For example (as shown in Figure 1 ), the hop factor for 2 since n3 is served as n88's nearest downstream clusterhead n8 becomes hopc(n8) ≥> 0. The purpose of based on the condition that hops(3%) hops(8%) 6— 4 In the following the factor is to fulfill the condition. using hop primarily connectivity n2 as

—

=

—

=

subsections, the three phases of the proposed ORC protocol

are

explained.

3.1. Route Discovery and Neighbor Information Collection The process of neighbor information collection employs the route request (RREQ) packets to collect the neighborhood information, which is executed at the same time with the route discovery process. Whenever a source node ns ∈ VG is required to communicate with the destination node ∈ VG for which it has no routing information in its routing table, ns initiates the route discovery process by broadcasting a RREQ packet. Upon receiving the first RREQ packet initiated by node ns, the intermediate node ni, ∈ VG will set up the reverse path and rebroadcast the packet if the route to nd is not available. Furthermore, node ni will calculate the distance between the sender of RREQ packet and itself according to the received signal strength of the packet. Since each intermediate node will receive and rebroadcast the RREQ packet, the neighborhood information of a node ni can be collected. It is noticed that the neighborhood information is maintained whenever the RREQ, the nd

reply (RREP), or the Hello packet is received or the data packet is overheard. As the route search packets are flooded into the cluster structure S ) which is constructed by another communication pair (i.e., the source e node and the corresponding destination node A s ), only certain nodes belonging to S are required to participate in the route discover

route

=

(

process. The cluster-RREQ (C-RREQ) packet, a variation of the original RREQ is created and broadcasted while the RREQ packet is received by a node nu ∈ V Figure 2 shows the structure of the C-RREQ packet. The CID

packet,

.

denotes the ID of the cluster that the C-RREQ packet is currently passing by; while the Neighbor_CID indicates the IDs of the neighboring clusters. As a node n receives the C-RREQ packet broadcasted by a node nu ∈ node nv will terminate the rebroadcasting action. On the other hand, if the node where Cx ≠ Cy, node nv will rebroadcast the C-RREQ packet associated with revision on both the CID and the Nieghbor_CID fields. As shown in V

,

nu ∈ V

Figure 2. The C-RREQ packet structure of the ORC protocol

Figure 3. The schematic diagram for route discovery within the cluster structure using the ORC protocol

Figure 3, the cluster C1 is the existed structure while the source node n4 intends to communicate with the corresponding destination node n5. The node n2 ∈ V will create and broadcast a C-RREQ packet after receiving the RREQ packet from the node outside its cluster C1. As node n3 ∈ V receives the C-RREQ packet sending from n2, node n3 will cease the rebroadcasting action since both nodes are in the same cluster C1. Upon receiving the C-RREQ packet, the clusterhead nx ∈ V fills in the Neighbor_CID field with the IDs of its neighboring clusters and continues to rebroadcast the C-RREQ packet to these clusters via the corresponding gateways. As the search packet leaves the clusters, the flooding search will be utilized to increase the chance for route discovery. As shown in Figure 3 node n6∈ V will initiate and broadcast the conventional RREQ packet to its non-clustered neighbors, e.g., node n7 ∈ y ,

.

3.2. Route Construction and Cluster Formation In the second phase, the routing path Ps,d and the cluster structure Ss,d will be constructed simultaneously. The functionality of the cluster-RREP (C-RREP) packet,

Figure 4. The C-RREP packet structure of the ORC protocol

a variation of the original RREP packet, is not only to construct the forwarding path for the route but also to help the nodes to contend for the clusterhead position. The contention result will therefore be recorded within the corresponding acknowledgment (ACK) packet. It is noticed that the ACK packet is obtained from the node’s medium access control (MAC) layer by extending one bit from its original packet header. The structure of C-RREP packet is shown in Figure 4, where the CH_Request is a flag utilized to request for clusterhead contention. A node which is expected to be the clusterhead sets the flag CH_Request to 1; otherwise the flag becomes 0. The Density field records the number of nodes located in the density area for the packet sender, i.e., |V | for sending node nj; while the Hop_Factor field represents the hop factor of the packet sender, i.e., hopc(nj). A RREQ (or C-RREQ) packet will eventually arrive at the destination node After a short period of the collection time, node nd will select a suitable route nd. according to the on-demand routing rules. The C-RREP packet will be initiated by node nd and unicasted back to its neighbor node from which it received the RREQ (or C-RREQ) packet. The process for cluster formation begins with the traversal of the C-RREP packet from node nd back to node ns. In order to reduce the energy consumption of the destination node nd, it is designed to be a cluster member instead of

a

clusterhead

or

cluster gateway.

The C-RREP packet keeps traversing the nodes along the reverse path which can be represented as the routing path Ps,d = ( V ). The intermediate node ni ∈ V will utilize the information obtained from the C-RREP packet to determine if the node nj ∈ V should become a clusterhead, where hops(nj) − hops(ni) = 1. The contention rules executed by node ni is shown in Algorithm 1, wherein the number of nodes located in the density area and the hop factor are considered as the two major criterions. The contending result will be delivered from node ni to node nj using the extended bit within the ACK packet. The extended fields of the C-RREP packet is recorded by node ni (i.e., lines 3–5 and 13–15 as in Algorithm 1) and the packet is unicasted to the node nk ∈ V for electing the clusterhead role, where hops(ni) − hops(nk) = 1. As shown in Figure 1, node n8 will unicast the C-RREP packet to node n2 after it executes the clusterhead election algorithm, wherein hops(n8) − hops(n2) = 4 − 3 = 1. As the C-RREP packet travels back to the source node ns, the routing path Ps,d and the cluster structure Ss,dcan be completely constructed. In order to consider the link reliability due to the dynamic movement of the nodes, it is required to exploit the Hello packets for periodic route maintenance. However, the excessive utilization of the Hello message will result in inefficient usage of the network bandwidth and increased control overhead. In the ORC protocol, it is proposed that only the nodes will periodically broadcast the Hello messages, which fulfill the partial nu ∈ V participation condition as mentioned in Section 2.

election algorithm Clusterhead election Algorithm 11 Clusterhead

Require: {«/, h;} 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16:

e

Vp(d

and

hops(nj)

—

hops(iij)

=

1

1 and | Vaj I > [ Va; I ) then if (hopc («|| ist 3) or (CH_Request accept node «/'s request to become a clusterhead 0 CH_Request -

l'\. Density Hop_Factor A- 1 *

else if CH_Re quest 0 then accept node u/s request to become end if if | Va./I < I Va/ I then -

Reject

node

a

cluster gateway

n/s request

end if 1

CH_Request Density

*

Hop_Factor

V'i. •«-

hopc(tij)

=

hopc(nj) +

1

end if

3.3. Route/Cluster Maintenance The third phase of the proposed ORC protocol is the maintenance for both the routing path Ps,d and the cluster structure Ss,d. Since the routing path is consisted of the clusterheads and the cluster gateways, the clusters and the routes can be maintained simultaneously. Both the active and the passive maintenances are considered in the proposed ORC algorithm. The active maintenance (also named as the handover process) hap∈V is lower than a per-defined threshold. pens while the energy of a node ni Assuming that node ni is the clusterhead of cluster Ci, ni will broadcast a request will be selected if it has the message searching for a new clusterhead. Node n shortest distance to ni and satisfies the connectivity condition for the cluster structure. In general, larger number of nodes in the density area of ni (i.e., larger | V |) corresponds to higher probability for recovering the cluster structure, wherein the adjacent relationship and the geographic location of clusters can remain unchanged. ,

On the other hand, the active maintenance for the cluster gateways is also addressed. It is considered that node ni, is denoted as the cluster gateway for the two clusters Cx and Cy, where nodes nx ∈ V and ny ∈ V are the corresponding clusterheads and hops(ny) hops(nx) > 1. Node ni will relinquish its cluster gateway position. In the mean time, the clusterhead nx will select another node n as the new cluster gateway according to the same rule for the clusterhead handover process, i.e., to fulfill the conditions of shortest distance and connectivity. —

The passive maintenance is implemented while a node ni ∈ V encounters unexpected fault or shutdown. If node ni is the clusterhead of cluster Ci, the

conventional local route repair scheme can be adopted for the election of the new clusterhead owing to its simple and efficient manner. On the other hand, it is considered that node ni is the cluster gateway for clusters Cx and Cy with nodes nx ∈ VCx and ny ∈ V as the two clusterheads and hops(ny) hops(nx) ≤ 1. For those nodes nj ∈ ( V ) that are connected with the cluster Cy are assumed to buffer the overheard data packets delivered from its own clusterhead nx. The buffered data packets will be dropped while nj overhears the corresponding ACK packet that is transmitted from the cluster gateway ni after a waiting time interval. If the node nj does not overhear the ACK packet from niafter a period of time, it will directly send its buffered data packet to the cluster Cy. Meanwhile, the clusterhead nx will overhear the data packet transmitted from nj to the cluster Cy, and therefore selects nj as the new gateway for the cluster Cx and Cy. —

4. Performance Evaluation The performance of the proposed ORC protocol is evaluated and compared with the AODV and the LID with AODV (LIDA) schemes via simulation. The LIDA protocol primarily executes the LID clustering algorithm associating with the AODV routing scheme. The simulations are conducted in the network simulator version 2 (ns-2. [ 17]) with wireless extension. The random waypoint mobility model is utilized for mobile nodes; while the IEEE 802.11 DCF is adopted as the MAC protocol in the simulations. The parameters utilized in the simulations are listed as shown in the Table 1.

Figures 5 and 6 show the performance comparison among these three protocols under different number of communication pairs (the average velocity of node 15 m/s). Figure 5 shows the control overhead obtained from these three schemes. In the LIDA protocol, the cost for cluster construction and maintenance is primarily constant during the simulation. It is observed that the control overhead of the LIDA scheme is reduced while the communication pairs are increased. On the other hand, =

Table 1. 1. Simulation Simulation parameters Table Parameter Type

Parameter Value

Simulation area Simulation time Transmission range Density area radius

1000

'

Traffic types Data rate Size of data packet Number of nodes Node velocity Communication pairs

x

1000

m

800 s 250 m 80 m Constant bit rate 4 packet/s 512 bytes 60 0, 5, 10, 15, 20 m/s 5, 10, 15,20

Figure 5. Performance comparison: control overhead vs. communication pairs (velocity = 15 m/s)

Figure 6. Performance comparison: end-to-end delay vs. communication pairs and packet arrival rate vs. communication pairs (velocity = 15 m/s)

the AODV

initiates the route discovery process by flooding the control structure. The control overhead is perceived to drastically increase flat packets as the number of communication pairs grow. In the proposed ORC algorithm, the cluster structure is established on-demand associated with the route discovery processes. It behaves similar to the flat routing scheme under smaller number of communication pairs; while the cluster-based structure is perceived with augmented number of communication pairs. Therefore, the control overhead and the end-to-end delay performance (as in Figures 5 and the left plot of Figure 6 ) of the proposed ORC protocol is closer to that from the AODV protocol under smaller number of communication pairs; while it converges to the cluster-based LIDA scheme as the number of communication pairs are increased. It is also noted that the comparably lowest control overhead is acquired via the proposed ORC algorithm while the number of communication pair is greater than 11 (as shown in Figure 5 ). As can be seen from the right plot of Figure 6 the packet arrival rate is decreased while the communication pairs are augmented. The proposed ORC and the AODV protocols outperform the LIDA algorithm under smaller number of communication pairs, i.e., with the number of communication pairs 5. Since the LIDA protocol executes the routing processes only after the cluster structure has been constructed, significant amounts of data packets will be dropped during the cluster formation period. On the other hand, the proposed ORC and the AODV scheme can both promptly execute the routing processes. Moreover, heavy traffic load is perceived within the network under the scenario of 20 communication pairs. It is observed that almost all mobile nodes participated in the routing process, which results in the increased probability of packet collision. No matter which scheme is adopted, the packet arrival rates are decreased to around 57% under the communication pairs 20. Figures 7 to 9 illustrate the performance comparison among these three protocols under different velocities (left plots: communication pairs 5; right plots: communication pairs 20). As expected, the routing performance (i.e., the packet arrival rate and the end-to-end delay) is degraded as the nodes’ velocities are increased. Furthermore, it is observed that the flat-based routing protocol (i.e., the AODV scheme) outperforms the cluster-based scheme (i.e., the LIDA algorithm)

protocol

over a

,

=

=

=

=

under smaller number of communication pairs. As the number of the communication pairs is enlarged, the performance obtained from the cluster-based routing protocol is comparably better than that from the flat routing algorithm. The performance of the proposed ORC protocol compromises between these two types of routing schemes. It can be seen from these plots that the performance obtained from the ORC algorithm consistently falls closer to the scheme with better performance under different communication pairs. The ORC protocol even surpasses the other two schemes in terms of the control overhead as the number of the communica20 (as in the right plot of Figure 7 ). The merits of using the ORC tion pairs scheme can be seen from these simulation results. The proposed ORC algorithm offers consistent routing performance under different level of traffic load within the networks. =

Figure 7. Performance comparison: control overhead vs. velocity

Figure 8. Performance comparison: end-to-end delay vs. velocity

Figure 9. Performance comparison: packet arrival rate vs. velocity

5. Conclusion In this article, an on-demand routing-based clustering (ORC) protocol is proposed, which simultaneously constructs the cluster structure and the routing path between the source and the destination nodes. The overhead induced from the cluster formation is minimized due to the on-demand characteristics in the proposed ORC protocol. The proactive and the passive maintenance schemes further enhance the robustness of the cluster structure. The merits of the proposed ORC scheme are evaluated via simulations.

Acknowledgments This work was in part funded by the MOE ATU Program 95W803C, NSC 962221-E-009-016, MOEA 96-EC-17-A-01-S1-048, the MediaTek research center at the National Chiao Tung University, and the Chung-Shan Institute of Science and Technology, Taiwan.

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Opportunistic Scheduling in Wireless Networks: A Feedback Load Perspective Yahya S. Al-Harthi King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia Email: [email protected] www.Harthi.net Abstract. With the ability to track the channel at the transmitter, adaptive transmission can be performed. Such tracking can happen via a feedback from the receiver. In multiuser systems, as the number of users who feedback their channel state information (CSI) increases, the spectrum resource that must be provisioned to carry this amount of feedback will create a large overhead on the system, which leads to an inefficient utilization of the bandwidth. In this article we propose an opportunistic scheduling algorithm that schedules users based on their channels qualities. The proposed algorithm reduces the feedback load while preserving most of the performance of opportunistic scheduling. In order to reduce the feedback rate, quantized values indicating the modulation level are fed back instead of the full values of the signal-to-noise ratios (SNRs). We consider the case where the users are independent and identical distributed (i.i.d.). The article also includes the derivation of closed-form expressions of the feedback load and system throughput. We compare the proposed scheduling algorithm under slow Rayleigh fading assumption with the optimal (full feedback load) scheduling algorithm. Keywords: Multiuser diversity, adaptive modulation, and feedback load.

1. Introduction With the emerging of new multimedia applications and the huge demand and growth for such applications, the need to provide high-speed high-rate transmission techniques is demanding. One approach to satisfy these requirements is to adapt the modulation and transmission power according to the instantaneous propagation conditions. With the ability to track the channel at the transmitter an increase in point-to-point capacity can happen by opportunistic communication, where transmission at high data rates take place in favorable channel conditions, and at low rates or not at all in bad channel conditions. Compared to the point-to-point settings, the multiuser settings offer more opportunities to exploit. It allows the system to benefit from a multiuser diversity. Multiuser diversity (MUDiv) is motivated by an information-theoretic result of Knopp and Humblet [1]. Knopp and Humblet focused on the uplink in single cell, with multiple users communicating to the base station via time-varying fading channel, which is assumed to be tracked at the receiver and information fed back to the transmitter. To maximize the total information-theoretic capacity, they showed that the optimal strategy is to schedule at any one time only the user with the best channel to transmit to the base station. Diversity gain arises from the fact that in a system with many users, whose channels vary independently, there

DOI: 10.1201/9781003336853-8

Opportunistic Scheduling in Wireless Networks

is likely to be a user whose channel is near its peak at any one time and by granting him the channel access the overall system throughput is maximized [2]. In the downlink from the base station to the mobile users similar results are obtained [3]. A scheduling algorithm exploiting the MUDiv is implemented as in Qualcomm’s High Data Rate (HDR) systems (1xEV-DO) [4]. In order to rank users in terms of channel quality, each user measures his instantaneous signal-to-noise ratio (SNR), with a help of a common broadcasted pilot, and feeds it back to the scheduler. One question rises when implementing such an algorithm is that: How much spectrum resources must be provided to carry this amount of feedback? This issue motivated researchers to propose new techniques to reduce the feedback load while exploiting diversity gain. In this article we address the issue of feedback load and develop a technique to reduce it while maintaining system performance.

2. Related Work The issue of feedback load has been addressed and many techniques were proposed. For instance, in [5], a scheduling technique was proposed, referred to as elective Multi-user Diversity (SMUD) scheduling in which each user compares his channel quality to a threshold. Only those who fall above the threshold are allowed to feedback their SNR measurements, while all others remain silent. The threshold was set to meet a specified outage probability. In [6], the work was extended, where the scheduler requests full feedback if none of the users’ channel qualities fall above the threshold. In addition, a set of switched-based multiuser access schemes were proposed in [7] in order to reduce the feedback load. In [8], multiple feedback thresholds were used to exploit MUDiv. In addition, a discrete rate switch-based multiuser diversity (DSMUDiv) scheduling scheme that rely on probing the users was proposed [9]. The scheme reduced the feedback load especially in the medium to high average SNR range while preserving the performance of opportunistic scheduling. A relay aided opportunistic scheduling (RAOS) scheme was proposed, which reduced the feedback load with the aid of relaying [10]. The RAOS scheme outperform the DSMUDiv scheme in terms of feedback load while no loss in capacity. In [11], a one-bit channel state feedback scheduling algorithm was proposed, where the scheduler uses these feedback bits to partition all users into two sets and assigns the channel to one user belonging to the set experiencing favorable channel conditions. Other techniques were developed and applied to multi-carrier systems. For instance, the work in [9] was extended to multi-carrier systems in [12]. To further reduce the feedback load and to guarantee a high probability of access the idea of enhanced equal access (EEA) scheduling policy suggested in [13], where scheduled users are removed from the scheduling processes of the remaining subchannels, was adopted. The scheme showed a reduction in the feedback load with little loss in the performance of opportunistic scheduling. In [14], an opportunistic scheduling scheme was proposed based on two partial channel state information (CSI)

4. Wireless Channel Model

reporting schemes: the best reporting scheme, each user reports the SNR of K subchannels having the highest instantaneous SNR, and the fixed reporting scheme, each user reports the SNR of K subchannels pre-determined during the initiation or handshaking process. In [ 15], a simplified feedback mechanism based on clustered orthogonal frequency division multiplexing (OFDM) was proposed. The idea is to let each user feed back information only about clusters that are instantaneously strong. Similar approach on clustered OFDM was proposed in [ 16], [ 17]. In [ 18], a switch-based reduced feedback OFDM multiuser opportunistic scheduling scheme was studied. In multi-antenna systems, feedback issue was investigated in [ 19 ], [20 ], [21 ]. To further reduce the problem of feedback load, decentralized channel-aware scheduling schemes were proposed in [22 ], [23 ], [24 ], [25 ], [26 ] based on the slotted ALOHA random access protocol [27 ], In addition, contention feedback schemes using multiple slots and spread spectrum (SS) feedback have been proposed to convey the CSI to the base station [28 ], [29 ]. Other work considered contention feedback schemes with reduced guard time [30 ], [ 31 ].

3. System Model We consider the downlink channel in a multiuser wireless system with K simultaneously active users served by one access point (AP), where interference from other cells is negligible. The transmitted signal from the AP can be received by all users in the coverage area. All the users are assumed to be synchronized to the AP, and incoming data are backlogged in the AP. The scheduling of the data is organized on a slot basis, with one and only one user accessing the channel during any given slot. We assume that estimation error is negligible and the feedback channel, which is from the user to the AP, is error free. The scheduling is based on channel quality, where the AP probes users and they feedback their CSI. The probing process can be done by broadcasting a pilot, which contains the ID of the intended user. In our study we consider a multi-level quadrature amplitude modulation (M-QAM) technique.

4. Wireless Channel Model The channel the users are communicating the AP through is wireless. This medium is harsh and is time-varying in nature. We consider fading channels, where the amplitude of the received signal varies randomly following a distribution function. Let the baseband channel model be, ri(τ) hi(τ) x(τ) = ni(τ) (1) +

·

where x(τ) ∈ C is the transmitted signal in time slot τ and $ ri (τ) ∈ C is the received signal of user in time slot τ. We assume that x(τ) has the same constant normalized transmitted power over time, i.e,, E The noise processes ni(τ) i

are independent and identical distributed (i.i.d.) sequences of zero mean complex Gaussian noise with variance a The fading channel gain from the AP to the ith user in time slot τ is hi(τ). We adopt a quasi-static fading channel model where hi(τ) is i.i.d. from burst to burst but remains constant over each burst. We consider a flat Rayleigh fading model, where the fading coefficients of all users are i.i.d. The amplitude of hi(τ), αi(τ) =|hi(τ)| is Rayleigh distributed with the probability density function (PDF) given by, fSubscriptalphaSubSubscript SubscriptBaselinel ft-parenthesi alphaSubscript BaselineSubscriptBaselineright-parenthesi equalsStarFaction2alphaSubscript BaselineSubscriptBaselineOvernormalup erOmegaSubscript BaselineSubscriptBaselineEndFractiontimes xptimesleft-parenthesi minusStarFactionalphaSubscript Superscipt2BaselineOvernormalup erOmegaSubscript BaselineEndFractionright-parenthesi tmes

(2) where a

is the short-term average

a

follows

an

fading power of the ith user.

The SNR,

exponential distribution, up er F Subscript gam a Baseline left-parenthesi gam a right-parenthesi equals left-parenthesi 1 minus e Superscript StartFraction egative gam a Over gam a overbar EndFraction Baseline right-parenthesi period

(3)

5. Channel Quality Based Scheduling 5.1. Algorithm In this article we consider channel quality based scheduling, where the user with the best channel quality is granted the channel access. Next, a description of our proposed scheduling algorithm and the optimal scheduling algorithm are presented. 5.1.1. Optimal Algorithm The optimal scheduling algorithm relies on full feedback from all users in the system. With K users in the system, the selection of the user will be as follows: (4) a

This selection strategy will result in the maximum multiuser diversity gain give K users in the system. One consequence in this strategy is the increase in overhead resulting from the full feedback of the channels qualities of the users. 5.1.2. Proposed Algorithm As shown in the previous section, to reach the maximum diversity gain we need to select the user with the maximum channel quality. Now putting this in mind, the question is, can we reach this diversity gain with the least feedback? Or can we reduce the feedback load while maintaining optimality? The answer to theses questions will be addressed next.

Before going to the description of the proposed algorithm, let’s define the followings: •

: Mn < Mn+1, 0 ≤ n ≤ N}, are discrete modulation levels, where 1 is the no transmission mode (outage) is, and MN is the highest modulation level. are quantized SNR values Q

M

=

M0

•

{Mn

=

=

a

(binary bits). q(n)represents

•

γ,

where γ ∈

(γ(n), γ(n+1))

and Mn is the modulation level.

The proposed scheme is a threshold-based scheme that selects the user with channel quality higher or equal to the threshold value (γth). At the guard time, which is between bursts, the AP begins in a random sequential fashion, probing users by sending a pilot. The user who is in order, according to the broadcasted sequence, will estimates the downlink channel quality, with the help of the pilot, and feedback the quantized SNR value (q). When this information is received at the AP one of the following actions will be taken: • Grant the user the channel access if q = q(N),or • Store the information and continue probing other users. brief, the AP will schedule the first

user it finds who has channel quality in modulation level or case no user is found with such channel MN support it will schedule the user will the channel quality highest quality compared to all users.

In

that

can

5.2. Analysis of the Overhead Load In wireless

transmission, two major components create significant sources of over(i) the overhead due to headers and/or trailers that are added to the frames or packets, which is called protocol overhead, and (ii) the overhead due to the control channel communication, which is called signaling overhead. In this article we are head:

concerned about the latter case. In this overhead, information about i.e., the channel quality or queue delay of different mobile users needs to be is sent to the AP, which grows with the number of users. It is important to analyze the scheduling algorithm in terms of overhead load to evaluate its performance.

Let’s define ρ to be the number of users who feed back their channels qualities (feedback load). In the optimal scheduling algorithm case, all users must feedback their channels qualities: ModifyingAbove rho With bar Subscript o p t Baseline left-parenthesis up er K right-parenthesis equals up er K period times

(5) Now by recalling the way the proposed algorithm works, only two reasons will enforce the algorithm to stop the Search process: (i) finding a user with channel quality exceeding or equal to the threshold value (q = q(N)). or (ii) all users are scanned. Let's set yth to be the threshold value, due to the behavior of the search process we can model it as geometric process, where the successful event is the event

when

with channel quality exceeding or equal to the threshold value is found. the Therefore, probability of a successful event at the /th search is: a user

(6)

P

where beta left-parenthesi gam a Subscript h Baseline right-parenthesi equals 1 minus up er P left-parenthesi gam a les -than gam a Subscript h Baseline right-parenthesi equals e Superscript StartFraction egative gam a Super Subscript h Superscript Over gam a overbar EndFraction

(7) is the complementary distribution function. In case no user is found with channel quality exceeding or equal to γth, which means all users are scanned. The probability of such event is: P

(8)

To derive the average overhead load or average feedback load, we need to take into account all possible situations. Therefore, the average overhead load is: ModifyingAbove rho With bar Subscript p r o p Baseline left-parenthesis up er K right-parenthesis equals normal up er Sigma Underscript i equals 1 Overscript up er K minus 1 Endscripts i p left-parenthesis i right-parenthesis plus up er K p left-parenthesis up er K right-parenthesis times period times

(9) A plot of the normalized average overhead load (i.e., the average overhead load divided by the number of users K) as a function of average SNR is shown in Figure 1 it can be observed that the proposed algorithm reduces the feedback significantly compared to the optimal algorithm at the medium to high average SNR range. The optimal scheduling algorithm needs feedback from all users to select the best user, which is why it has the highest normalized average feedback load (equal to 1). The reason that at low average SNR values the need for full feedback is observed is due to the selection of γth. In this figure, higher than 11 dB average SNR value will lead to a successful event, finding a user exceeding or equal to γth. As we increase Yth, the breaking point (the point on the average proposed algorithm decreases) will increase.

SNR axis at which the

plot

of the

5.3. Analysis of the Scheduling Delay Both algorithms described above are polling-based scheduling algorithms. Basically, respond to the probing by feeding back their channels qualities. The process of polling this information will cause certain time delay that starts at the beginning of the first probe and ends at the time a user is scheduled. We can see that such a mechanism will last longer as the number of users increases for a given channel condition. To measure the performance of both algorithms we investigate the effect of the scheduling delay on the system performance. users

Figure 1. Normalized average overhead load vs. the average SNR for (i) optimal scheduling algorithm, and (ii) proposed scheduling algorithm. K = 25

Let’s define the following: • Guard time (τg): The time period that the scheduling process takes place, which is between bursts. • Polling Delay (τp): The time it takes to collect and process the information of one user, which we assume it is the same for all users. In the proposed scheduling algorithm, the number of users searched until a is scheduled is a random number, which depend on the threshold value and the average SNR value. In this algorithm, the guard time duration equals to the time it takes to schedule a user, which introduce a randomness in the guard time length, τg = {i ·τp : 0 ≤ i ≤ K}. Such variation in length can be beneficial by better utilizing the resources and that can be done by dynamically allocating the spectrum. It can be seen clearly that the average guard time is equal to the average scheduling delay, which is: user

tau overbar Subscript g Baseline left-parenthesi l right-parenthesi Subscript p r o p Baseline equals ModifyingAbove rho With bar left-parenthesi l right-parenthesi dot au Subscript p dot Subscript

(10) where l is the number of users in the system.

In the optimal scheduling algorithm case, the average guard time is: tau overbar Subscript g Baseline left-parenthesis l right-parenthesis Subscript o p t Baseline equals l dot tau Subscript p dot

(11) 5.4. Analysis of the System Throughput After analyzing the scheduling delay, we will investigate the impact of the scheduling delay on the system throughput. The system throughput is defined as the amount of bits transmitted per unit time, where this time includes the data transmission time (Td) and the guard time (τg), per unit bandwidth in bits/sec/Hz for specified power and target error performance.

In this article, the adaptive M-QAM scheme is assumed. Specifically, we consider a transmission scheme employing uncoded adaptive discrete rate M-QAM schemes with constellation sizes Mm = 2m for m ∈ Sm ={0, 1, 2,...,N}. With good channel condition higher modulation levels can be selected, on the other hand, as the channel condition degrades the modulation levels also degrades. The transmission rate at time slot t will depend on the selected user. Because both algorithms are channel quality based algorithms, selecting the best user, the system capacity will reach the maximum, for a given number of active users in the system. If we denote the target average bit error probability (BEP) by BEP0, M-QAM thresholds or switching thresholds can be obtained according to [eq. (30), (32)]: gamma Subscript h Superscript left-parenthesis 1 right-parenthesis Baseline equals left-bracket e r f c Superscript negative 1 Baseline left-parenthesis 2 dot up er B up er E up er P Subscript o Baseline right-parenthesis right-bracket squared comma

gamma Subscript t h Superscript left-parenthesis n right-parenthesis Baseline equals minus two-thirds left-parenthesis 2 Superscript n Baseline minus 1 right-parenthesis times ln left-parenthesis 5 period times upper B upper E upper P italic 0 right-parenthesis times semicolon n equals 2 comma 3 comma ellipsis comma upper N comma

gamma Subscript h Superscript left-parenthesis upper N plus 1 right-parenthesis Baseline equals plus infinity

where erfc−1(·) denotes the inverse complementary error function. The selection of the user is based on (4) therefore, the average system capacity is: ,

StartFraction left pointing angle up er C right pointing angle Superscript asterisk Baseline Over up er W EndFraction equals integral Subscript minus infinty Superscript plus infinty Baseline log Subscript 2 Baseline left-parenthesi 1 plus gam a Superscript asterisk Baseline right-parenthesi f Subscript gam a Sub Superscript asterisk Subscript Sub Superscript Subscript Baseline left-parenthesi gam a right-parenthesi times d gam a period times

(12) Because we consider discrete rates, the average system capacity can be found from [9]: StarFactionleftpoint gangleup erCrightpoint gangleSupersciptasteriskBaselineOverup erWEndFractionequalsup erRleft-parenthesi up erKright-parenthesi equalsup erB0timesperiodtimesleft-parenthesi 1minusbetaleft-parenthesi gam aSubscript hSupersciptleft-parenthesi 1right-parenthesi Baselineright-parenthesi rght-parenthesi Supersciptup erKBaselineplusnormalup erSigmaUndersciptnequals1Oversciptup erNminus1Endscriptsup erBSubscriptnBaselinetimesperiodtimesleft-parenthesi left-parenthesi 1minusbetaleft-parenthesi gam aSubscript hSupersciptleft-parenthesi nplus1right-parenthesi Baselineright-parenthesi rght-parenthesi Supersciptup erKBaselineminusleft-parenthesi 1minusbetaleft-parenthesi gam aSubscript hSupersciptleft-parenthesi nright-parenthesi Baselineright-parenthesi rght-parenthesi Supersciptup erKBaselineright-parenthesi plus p erBSubscriptup erNBaselinetimesperiodtimesleft-parenthesi 1minusleft-parenthesi left-parenthesi 1minusbetaleft-parenthesi gam aSubscript hSupersciptleft-parenthesi up erNright-parenthesi Baselineright-parenthesi rght-parenthesi Supersciptup erKBaselineright-parenthesi periodtimes

(13)

where Bn = log2 Mn is the number of bits per constellation.

Figure 2. Average system throughput vs. the average SNR for (i) optimal scheduling algorithm (τp = 0.001Td, and τp = 0.01Td), and (ii) proposed scheduling algorithm (τp = 0.001Td, and τp = 0.01Td). K = 25

Both algorithms will provide the same system capacity and that is understood because both of them will end up scheduling the best user. The above expression is only taking into account the amount of bit transmitted in Td. To derive the system throughput, which takes into account the scheduling delay, we include the ratio of the a to Td in the system capacity expression. Therefore, the average system throughput is: up er S overbar equals left-bracket left-parenthesi StartFraction up er T Subscript d Baseline minus ModifyingAbove tau With bar Subscript g Baseline left-parenthesi up er K right-parenthesi Over up er T Subscript d Baseline EndFraction right-parenthesi times up er R left-parenthesi up er K right-parenthesi right-bracket

(14) where in case the optimal algorithm ModifyingAbove tau With bar Subscript g Baseline left-parenthesi up er K right-parenthesi equals left-brace Subscript au overbar Sub Subscript g Subscript left-parenthesi up er K right-parenthesi Sub Subscript o p t Subscript imes i n times c a s e times t h e times o p t i m a l times a times log base 10 o r i t h m times period times Superscript au Super Subscript g Superscript overbar left-parenthesi up er K right-parenthesi Super Subscript p r o p Superscript imes i n times c a s e times t h e times p r o p o s e d times a times log base 10 o r i t h m com a Baseline times

A

plot of the average system throughput as a function of the average SNR is Figure 2. Note that to observe exactly the effect of delay we need to test the algorithm experimentally, which is out of the scope of this article. We just consider

shown in

percentage values. We

set the data transmission time slot

(Td) to

one

time unit and

A list 10 2) Table 1. 1. A list of of selected selected modulation modulation levels levels (BEPo (BE If, = 10−2) Table =

Modulation Level

Switching Threshold (dB)

BPSK

4n=4.8

4-QAM 16-QAM 64-QAM

r*

-

-

7.8 15

4'=20

set the polling delay (τp) to δTd, where δ is the ratio of the polling time delay to the data transmission time. We can observe the effect of the delay on the system throughput. For a given value of τp, our proposed algorithm performs better than the optimal algorithm and that is due to the reduction in the number of users who feedback their SNRs, while still selecting the best user. As we increase τp the optimal algorithm will experience bigger loss in throughput, while our proposed algorithm will experience little degradation in throughput.

6. Summary The aim of this chapter is to present an opportunistic scheduling technique, which is channel equality based, that reduces the feedback load while minimizing the loss in throughput. We first gave a brief literature review of the most important work done in this area. Then we described the system and channel models. After that, we described our proposed scheduling algorithm and the way it works. We also mentioned how the optimal scheduling algorithm works for comparison reasons. Then an analytical description of both the proposed and the optimal algorithms were presented, where we derived the closed-form expressions of the average feedback load and the average system throughput. Based on the numerical examples, we saw that the polling process will affect the system throughput due to the introduced delay. We also saw that our proposed scheduling algorithm reduced the feedback load compared to the optimal scheduling algorithm.

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Cross-Layer Optimization for Upstream TCP Flows in IEEE 802.11 Wireless LANs Nakjung Choi a,1, Jiho Ryua , Yongho Seokb , Taekyoung Kwona and Yanghee Choi a a Seoul National University, Seoul, Korea b LG Electronics., Seoul, Korea Abstract. This chapter via analysis and simulation revisits the interaction between MAC contention and TCP congestion control over IEEE 802.11 wireless LANs, misled in the previous efforts. The results reveal that the effective number of contending wireless stations is not proportional to the number of wireless stations with an upstream TCP flow in IEEE 802.11 wireless LANs. Thus, we propose a new scheme called TCP ACK Priority (TAP) in which, by allowing an access point to transmit TCP ACKs at the highest priority, an optimal number of competing stations are allowed to contend for media access to utilize link bandwidth efficiently. We use an ns-2 simulator to evaluate the performance of TAP with the IEEE 802.11 DCF. The results show that there is an improvement in network performance without the loss of fairness between upstream TCP flows. The extensions for IEEE 802.11e/n are also considered. Keywords: Wireless LAN, IEEE 802.11, TCP, Interaction, Effective contending stations.

1. Introduction Most Internet applications use TCP, but it performs poorly in wireless environments. Thus, there have been several efforts to improve TCP performance in distributed wireless networks such as IEEE 802.11 wireless LANs [ 1 ]. However, previous authors have blindly assumed that the number of stations (STAs) competing at the MAC layer is proportional to the number of STAs with a TCP flow, which is not true under congested network conditions. This is because TCP has a congestion control mechanism [4 ] consisting of two phases: slow start and congestion avoidance. In the slow start phase, a congestion window (cwnd) is initialized to one segment when a new TCP connection is established. Each time a TCP ACK is received, cwnd is increased by one segment, resulting in an exponential increase in the window size for every round trip time (RTT). After cwnd reaches the slow start threshold (ssthresh), the congestion avoidance phase starts, in which cwnd is incremented by 1/segment after each RTT, resulting in a linear increase in the window size. Note that when a STA has sent cwnd of TCP data, it cannot send more data until it receives a TCP

1 Corresponding Author: Nakjung Choi, Building 138 Room 317, Seoul National University, San 56-1, Shillim-dong, Kwanak-gu, Seoul, Korea, 151-742., e-mail:[email protected]

DOI: 10.1201/9781003336853-9

Optimizing Aggregate Throughput of Upstream TCP

ACK from the recipient. Therefore, a STA waiting for a TCP ACK cannot contend for channel access at the MAC layer. In a congested wireless LANs, the result is that only a small number of wireless STAs that wish to send TCP data will effectively contend for wireless channel access, while most of the STAs cannot transmit TCP packets due to cwnd limitations. It is normally assumed that each STA and an access point (AP) will get a fair share of the wireless channel capacity in the long term. After a STA transmits TCP packets of cwnd size, it cannot attempt to transmit the next TCP packet until it receives a TCP ACK. That is, after the AP transmits a TCP ACK to the STA, the STA will compete with the AP (and other STAs, if any) for wireless channel access. Our empirical study in Section 3.1 reveals that the number of competing STAs at the MAC layer is mostly around two regardless of the number of STAs with an upstream TCP flow. However, the number of competing STAs should be increased to achieve an optimal aggregate throughput in IEEE 802.11 wireless LANs. The remainder of this chapter is organized as follows. In Section 2, we introduce previous research on improving the TCP performance over wireless networks. Then, we analyze why the performance problem takes place in case of TCP over IEEE 802.11 wireless LANs and propose our mechanism called TCP ACK Priority (TAP) to enhance the aggregate TCP throughput in Section 3. Section 4 presents simulation results in terms of the effective number of competing STAs, aggregate throughput, fairness index and delay. Finally, we conclude our work in Section 5.

2. Related Work I-TCP [ 5 ] uses a split-connection approach. It divides a TCP connection into two distinct connections: a wired connection between a fixed host and an AP, and a wireless connection between an AP and a wireless STA. When the AP receives a TCP data packet through the wired connection, it sends a TCP ACK corresponding to the TCP data packet back to the fixed host and transfers the TCP data packet to the wireless connection. The main advantage of this approach is that transmission errors over wireless links can be hidden from the TCP sender, which is in the wired part of the network, and TCP over the wireless link can be optimized independent of the wired connection. However, it has the disadvantage that it violates the end-toend semantics of TCP. For example, a TCP ACK may be delivered to a TCP sender before the associated TCP data is actually delivered to the TCP recipient. In another study [6 ], a TCP snoop protocol makes changes to the network layer by introducing a new module called a snoop agent at an AP. This agent buffers TCP data packets which are destined for wireless STAs and which have not yet been acknowledged by them. When the loss of a packet is detected by the arrival of duplicated TCP ACKs, or by TCP timeout, the agent performs local retransmission across the wireless link. This scheme also prevents the TCP sender from invoking unnecessary fast-retransmission by dropping the duplicated TCP ACKs at the AP. It improves on the split-connection approach by preserving the end-to-end semantics and using the soft-state at an AP.

3. Optimizing the Effective Number of Competing Stations DCF+ [7 ] is a recent approach to enhancing TCP performance over wireless LANs. DCF+ is based on the WLAN MAC layer, and extends IEEE 802.11 DCF while remaining compatible with it. DCF+ assumes that a recipient has a data frame ready to be transmitted back to the sender. Standard DCF requires that a source STA transmitting a data frame must receive a MAC ACK frame from the destination STA. DCF+ makes the ACK frame act as an RTS frame sent by the destination. Then, the source replies with a CTS and the destination can immediately transfer data frames which are ready to send to the source STA. This procedure ensures that the next transmission in reverse direction follows without contention, and hence reduces the time required for successful transmission.

When several mobile hosts upload packets using TCP, flows with only a small number of packets in flight (e.g. newly started TCP flows) are more susceptible to timeouts than flows with a large number of packets in flight. Small flows can therefore be starved for a long time due to timeouts induced by packet losses. This unfairness of upstream TCP flows can be resolved by using additional flexibilities of the IEEE 802.11e MAC, which allows the values of interframe space (IFS) called Arbitrary IFS (AIFS) and CWmin to be set on a per-class basis for each wireless STA. STAs with small values of IFS and CWmin have more opportunities for packet transmissions. By reducing IFS and CWmin for an AP, and increasing them for other wireless STAs, the AP gets a more equitable share of opportunities to access the wireless channel [8].

3. Optimizing the Effective Number of Competing Stations 3.1. TCP over IEE 802.11 wireless LAN In order to understand why TCP performs poorly in IEEE 802.11 wireless LANs, we need to know that TCP flows in IEEE 802.11 wireless LANs have little to do with network congestion. According to [10] that analyzes the saturation throughput of the IEEE 802.11 DCF, as the number of active STAs2 increases, the saturation throughput of IEEE 802.11 wireless LANs decreases. However, [9] presented different experimental results that the aggregated throughput of TCP flows is stable even though the number of STAs increases. The reason is that the number of active STAs is nearly the same independently of the number of STAs with a TCP flow. Since TCP adopts a window-based flow control mechanism, a TCP sender does not have any TCP DATA packet to send until it receives TCP ACK packets for transmitted TCP DATA packets. In this situation, the number of active STAs is much smaller than the number of STAs. To simplify an analysis of this window-based flow control mechanism of TCP in IEEE 802.11 wireless LANs, we assume that all STAs and an AP get a chance to 2 A STA can be classified into an active or inactive one. An active STA is defined as a STA having at least one frame to send and participating in the wireless channel contention, while an inactive one does not try to send any frame.

Figure 1. An n-state Markov chain for upstream TCP flows in IEEE 802.11 wireless LANs

Figure 2. Ratio of competing active STAs

transmit a frame in a round-robin manner due to the fairness of the IEEE 802.11 DCF. Figure 1 depicts a simple n-state Markov chain that models upstream TCP connections in the IEEE 802.11 infrastructure mode. N STAs are trying to upload TCP DATA packets to N fixed hosts via an AP. We assume that each STA has an average of W TCP packets to upload. We devote the state of the network as b(L1, L2), where L1 is the sum of the lengths of the queues at all STAs and L2 is the length of the queue at the AP. After a STA has transmitted W TCP packets, it cannot contend to transmit another TCP packet until it receives a TCP ACK packet from the AP. By running MATLAB with this model until it reaches a steady state, we determined the probability density function of the number of active STAs participating in the wireless channel contention, and these results are plotted in Figure 2(a). This graph shows that the number of active STAs is mostly less than five regardless of the number of STAs that are trying to upload TCP DATA packets, so the network is never saturated. These analytic results explain why the number of STAs does not affect the aggregate throughput of TCP flows in IEEE 802.11 wireless LANs. Our empirical study using an ns-2 simulator [ 11 ] verifies this analysis, as shown in Figure 2(b) However, the number of competing STAs should be increased to achieve an optimal aggregate throughput in IEEE 802.11 wireless LANs. .

3.2. TAP: TCP ACK Priority We propose to modify the mechanism of MAC-layers contention so as to increase the number of competing STAs in order to achieve a higher aggregate TCP throughput. Suppose that the maximum aggregate throughput of a wireless LAN can be achieved when n* STAs (including an AP) contend to access the wireless channel. IEEE 802.11 DCF specifies that a STA should perform random backoff for collision avoidance even if there is only one STA in the network. The waste of link bandwidth due to this backoff time is reduced when several STAs are competing for wireless channel access. However, as the number of STAs increases, the increasing frequency of frame collisions degrades the aggregate network throughput. Between there extremes is the optimal number of competing STAs, and we will propose a method of ensuing that this number is achieved in practice. In our proposed mechanism called TCP ACK Priority (TAP), the AP transmits 1 STAs in a way that preempts all other transmissions. This TCP ACKs to n* can be achieved if the AP intentionally transmits at the 0thslot after a DIFS, with —

backoff time. In order to choose an appropriate value of n*, we have used the throughput analysis of 802.11 DCF wireless LANs by Bianchi [ 10].

no

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Where, τisthe probability that a STA transmits in a randomly chosen time-slot and p the conditional collision probability. A frame being transmitted on the channel has a probability ρ of experiencing a collision. Tc is the time wasted due to a packet collision in a basic access (DATA/ACK) or optional access (RTS/CTS/DATA/ACK) mechanism. For more details about these equations, please refer to Equations (7) , (9) and (28) in [ 10]. From these equations we can determine compute the number of STAs which achieves the maximum throughput. Figure 3 shows the optimal number of competing STAs as the sizes of transmitted frames (the sizes of MAC service data units) changes. There are four different bit rates and two access mechanisms. For the purpose of this analysis, all STAs using the basic access mechanism are assumed to have the same data rate. In the basic wireless LAN access mechanism, the collision time is determined by the longest transmission time ((DATA / Data Rate)*) of all STAs involved in a collision; and we can also see that the optimal number of STAs varies depending on the data rate and the frame size. As the data rate increases and the frame size decreases, the

Figure 3. The optimal number of STAs for the maximum

optimal number of STAs becomes larger because the frame transmission time is shorter and so the time wasted due to frame collisions is reduced. However, when the RTS-CTS access mechanism is used, the optimal number of STAs is fixed at 7.526. In this case collision times do not depend on the data rate or on the size of the data frame, since collisions can only occur during RTS-CTS handshaking when a fixed frame size and the basic rate are being used. From Figure 3, we can conclude that n* should be let adaptively to a value between 1 and 8, depending on the data rate of the STAs, the average size of the frames being transmitted and the type of the channel access mechanism. To incorporate TAP into wireless LANs without any modification to IEEE 802.11, we can utilize the new features of IEEE 802.11e/n. The AP can transmit multiple TCP packets successively by using the Transmission Opportunity (TXOP) feature of the IEEE 802.11e standard [2], or the multi-destination frame aggregation facility that is discussed in the IEEE 802.11n draft [3]. After the AP obtains the wireless channel, as described above, sufficient TXOP to transmit n* − 1 TCP packets is given to the AP, as shown in Figure 4(a). Alternatively, several MAC Protocol Data Unit (MPDU) frames involving TCP ACK packets for each STA can be integrated into a single MPDU, which is then transmitted by the AP, as shown in Figure 4(b). Although multi-destination frame aggregation can avoid overheads such as the need for a SIFS and a MAC header for each TCP packet, several TCP flows will all be interrupted if the aggregated frame is lost.

Figure 4. TAP operation for prioritizing TCP ACK packets

4. Performance Evaluation We evaluated TAP using the ns-2 simulator. The simulated network topology consists of n STAs and an AP in the wireless part of the network and n hosts in the wired part, where n is a variable. Each wireless STA is sending TCP traffic to the corresponding host. The AP and n STAs compete to transmit TCP ACK and TCP DATA packets, respectively. We use the FTP traffic model with 1024-byte TCP DATA packets and every TCP DATA packet is transmitted at 11 Mbps with or without an RTS/CTS mechanism. If an RTS/CTS mechanism is enabled, the RTS/CTS frames are transmitted at 1 Mbps. The total simulation time is 200s in all cases, and we compare IEEE 802.11 DCF and TAP using four performance metrics: the probability density function of the number of active STAs, aggregate throughput, fairness index and delay. The value of n* is set to 8 for the RTS/CTS mechanism and to 4 for the basic access mechanism (see Figure 3 ).

Figure 5(a) shows how the probability density function of the number of active STAs depends on the number of TCP flows with no RTS/CTS. The average number of active STAs in 802.11 DCF stays around 2 while the number of active STAs in TAP is about 4, which are almost optimal values with these conditions. Figure 5(b) shows that TAP achieves higher aggregate throughput by making 8 STAs compete for the wireless channel access with the RTS/CTS mechanism and 4 with the basic access mechanism. Figure 6 shows how the long-term fairness (Jain at el, [12]) changes with the number of TCP flows. In IEEE 802.11 DCF, a TCP sender cannot transmit any TCP DATA packet until it receives a TCP ACK packet, while in TAP, several TCP senders receive TCP ACK packets, which are transmitted with higher priority, so that a short-term fairness problem may occur. However, this result reveals that there are no long-term fairness problem since the fairness index stays around 1 with both the IEEE 802.11 DCF and TAP.

Figure 5. Improvement on the performance of TAP

Figure 6. Fairness between upstream TCP flows

We observed that two behaviors in TAP: (a) more active STAs compete, which results in more collisions and longer delays, and (b) the AP transmits TCP ACK packets with higher priority, which increases TCP DATA packets’ delay. Hence, TAP has a little bit increased latency. However, recall that the number of the active STAs is kept as 4 in TAP and 2 in IEEE 802.11 DCF, thus the average delay is maintained almost stable regardless of the number of STAs in the wireless LAN.

5. Conclusion Our analysis and simulation results suggest that previous models of competing TCP flows in IEEE 802.11 wireless LANs are misleading. We have analyzed the interaction between MAC contention and TCP congestion control. By introducing prioritized access by the access point, the proposed scheme makes the optimal number

of competing stations contend for media access. Through ns-2 simulations we have demonstrated that our proposal can achieve a higher aggregate TCP throughput than the original IEEE 802.11 DCF at the cost of slight delay increase.

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Cooperative Communication for Energy Efficient Wireless Sensor Networks Ljiljana Simic´1, Stevan M. Berber and Kevin W. Sowerby Department of Electrical and Computer Engineering, The University of Auckland, Auckland, New Zealand Energy efficient communication is a key requirement of energy-constrained wireless networks. In this chapter we show that cooperative communication can be deployed in wireless sensor networks as an effective practical energy saving technique. In cooperative communication a partner node is recruited to help with communicating a source node's message by overhearing and repeating it to the destination receiver. We present an energy analysis of cooperation to demonstrate that cooperative communication has the potential to significantly reduce the total energy cost of wireless Communication, provided the transmission range is beyond a certain threshold. We examine the feasibility of practically exploiting this energy saving potential in a wireless sensor network by considering the energy savings achieved for a given source node cooperating with a range of potential partners, using optimal power allocation for the cooperative transmission. We demonstrate that the partner choice region for energy efficient cooperation is large relative to the source-destination separation, meaning that significant energy savings can be achieved in practice from cooperation with a wide range of partners. We present a simple distributed cooperation protocol for wireless sensor networks, whereby each source node autonomously makes cooperation decisions based on a simple yet near-optimally energy efficient cooperation strategy. We thus show that large network-wide energy savings can be attained via cooperative communication without the need for central coordination.

Abstract. sensor

Keywords: Wireless Sensor Networks Energy Efficiency Cooperative Diversity.

1. Introduction Wireless sensor networks have become a key technology of the early 21st century, with a multitude of applications such as environmental control, habitat monitoring, logistics, machine monitoring and agriculture [1]. These networks consist of many small distributed wireless sensor nodes. Each node has integrated sensing, computation and communication capability, enabling distributed sensing of a physical phenomenon [2]. The inherent challenge of developing a wireless sensor network is simultaneously accommodating many conflicting demands; small low-cost sensor nodes must operate efficiently and reliably for a very long time, powered by small batteries which are typically never replaced [3 ]. Consequently, low energy consumption is one of

1 Corresponding Author: Ljiljana Simić, Department of Electrical and Computer Engineering, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand; e-mail: [email protected]

DOI: 10.1201/9781003336853-10

Cooperative Communication for Energy Efficient Wireless Sensor Networks

the key requirements of wireless sensor networks. Energy efficient communication is thus a central concern in sensor network design. Wireless communication is typically severely impaired by the phenomenon of signal fading, which is due to multipath propagation of radio signals [4]. The performance of communication systems in fading wireless channels can be greatly improved by employing diversity techniques, such as multiple transmitting and receiving antennas [5]. The diversity benefit of achieving reliable communication at a much lower transmission energy cost is very desirable in energy-constrained wireless sensor networks. However, the small size and low complexity requirements of individual sensor nodes preclude the direct implementation of multiple antenna arrays. Recent work on cooperative transmit diversity techniques [ 6] [ 9] has shown that spatial diversity gains are possible without the need for a physical antenna array at the transmitter. Instead, spatial diversity is achieved via cooperative antenna sharing among transmitting partner nodes. In cooperative communication a partner node overhears and repeats the source node's transmission to a destination receiver; diversity gains result from the destination receiver combining these two signals sent over independently faded paths. Thus cooperative diversity can be applied to wireless sensor networks to reduce node energy consumption. Cooperation is an intuitively pleasing concept for wireless sensor networks, where individual nodes inherently work towards a common goal. Furthermore, while

simple and individually have limited capability, they are cooperation recognizes this ‘strength in numbers’ as a major and important resource that ought to be exploited to the network’s advantage. Thus using a partner node’s energy to improve the energy efficiency of communication for another node is an apt way of better exploiting the combined resources of the network. Our goal in this chapter is to argue that cooperative communication can be deployed in wireless sensor networks as an effective energy saving technique. We present an energy analysis of cooperation to demonstrate that cooperative diversity has the potential to dramatically reduce the total energy cost of wireless communication in sensor networks. Furthermore, we show that it is feasible to practically exploit this energy saving potential in a wireless sensor network by way of a simple and flexible cooperation protocol. The protocol is based on a simple cooperation strategy that allows sensor nodes to autonomously make cooperation decisions leading to near-optimal energy efficiency. sensor

nodes

are

numerous;

2. Cooperative Diversity for Wireless Sensor Networks In a typical wireless sensor network, sensor nodes wirelessly transmit information they have collected from the environment to a destination receiver, which may be a remote central processor or another node in a multi-hop network. In cooperative communication a partner node is recruited to help with communicating the source node’s message by overhearing and repeating it to the destination (Figure 1). Several different cooperative diversity schemes have been proposed in the literature,

2. Cooperative Diversity for Wireless Sensor Networks

Figure 1. Decode-and-forward cooperative communication: the partner node overhears and repeats the source node’s original transmission to the destination receiver, where the two signals sent over independently faded paths are combined, resulting in diversity gains and may be generally classed into one of two basic approaches: a virtual antenna array in the form of virtual-MISO [ 10] or ‘cooperative relaying’ in the form of decode-and-forward [S]. The latter has been shown to be especially suitable for wireless sensor networks due to its superior energy efficiency and low implementation complexity [ 11 ]. In this

chapter, we consider the selection decode-and-forward [8 ] cooperative which operates as follows. The source’s transmission to the destischeme, diversity nation is also received by the partner in the first phase. In the second phase, there are possible cases regarding the partner’s participation in the cooperative transmission. If the partner is able to decode the source’s message correctly, as determined by a CRC check, it forwards it to the destination; otherwise, the partner does not retransmit and the destination only receives the source’s original transmission. The overall end-to-end BER (bit error rate) of the cooperative system, BERcoop, may be expressed as the weighted sum of the BERs of these two cooperative cases, two

BERcoop

=

BLERs-p BERnon_coop

+

(1

—

BLERs_p)BERfull-coop,(1)

where BLERs−p is the BLER (block error rate) of the source-partner transmission, BERnon_coop is the BER of the source-destination non-cooperative transmission, and BERfull_coop is the BER of the cooperative diversity transmission of the source and partner to the destination [12]. We assume that optimal diversity combining is used at the destination receiver and that uncoded BPSK modulation is used for all transmissions. The source-destination, source-partner, and partner-destination communication channels are assumed to be independent flat Rayleigh slow fading channels [8], [9]. Figure 2 shows the BER curve of selection decode-and-forward cooperation for a BPSK system in Rayleigh fading, plotted versus the average received signal-to-noise ratio (SNR) at the destination receiver, for three different values of BLERs−p. The BER performance of a cooperative system with a blocked sourcepartner channel (BLERs−p = 1) is equivalent to that of a non-cooperative system, namely BERnon_coop. Conversely, an ideal source-partner channel (BLERs−p = 0) enables full cooperation whereby second-order diversity is achieved at the destination receiver, with BERcoop = BERfull_coop. Finally, for BLERs−p = 0.1, the BER curve of the cooperative system is shown to be a weighted combination of these two extreme cooperative cases, as indicated by (1). Figure 2 shows that the BER curves of systems with successful cooperation (BLERs−p < 1) are below that

Figure 2. BER of selection decode-and-forward cooperation vs. average received SNR at the destination receiver, for different values of BLERs−p, the block error rate on the source-partner channel. BLERs−p = 1 corresponds to a non-cooperative transmission, whereas BLERs−p = 0 means that the partner always correctly decodes and forwards the source’s message, resulting in full second-order diversity at the destination receiver. BLERs−p = 0.1 means that 90% of the source’s messages are correctly decoded and forwarded by the partner of the non-cooperative system. Therefore, employing cooperation clearly reduces the total transmission energy required for a given reliability of communication. Furthermore, it is evident from Figure 2 that a significant reduction in total transmission energy is achieved by cooperation even when the source-partner channel is non-ideal (BLERs-p 0.1). This flexibility further demonstrates that selection decode-and-forward is a practically suitable scheme for wireless sensor networks, capable of extracting energy saving benefit from cooperation with a variety of (poten—

tially non-ideal) partners.

3. Energy Efficiency of Cooperative Communication The total energy

of wireless communication consists of two domicost and the transceiver circuit energy consumption. We have shown in the previous section that cooperation reduces the transmission energy cost of communication. However, cooperation involves an extra radio transceiver by way of the partner, thereby increasing total circuit energy consumption in communicating the source’s message. In this section we quantify both of these dominant energy elements in order to show that cooperation can provide significant energy savings in a wireless sensor network, even when the additional circuit energy overhead is taken into account. nant

consumption

components: the transmission energy

The total average power consumption of a short-range communication system may be expressed as the sum of the total power consumption of the RF power amplifiers PPA and the total power consumption of all other transceiver

circuit blocks PCCT [10]. The first term PPA is directly proportional to the transmit power Pout, Pout LEbRb, (2)=

where Eb is the required energy per bit at the receiver for a target BER pb, Rb is the bit rate, and L is the channel path loss and may be calculated according to the log-distance path loss model, L

= dk Lref,(3)

where d is the transmission distance, k is the channel path loss exponent, and Lref is the reference path loss at a reference distance of lm [4 ], The second term PCCT is the sum of the power consumed in the transmitter circuit blocks, PCCT_tx, and the power In our subsequent analysis, we use consumed in the receiver circuit blocks, PCCT_rx. PCCT_tx

=

98.2mW, PCCT_rx

=

109.5mW, Lref

pb = 10-3. For further details of this power and the references therein.

≡ 90dB, k

=

3.5,

consumption model

Rb

=

please

and refer to [ 12]

10kb/s

It follows that the total energy consumption per information bit using noncooperative communication may be expressed as = Enon_coop

(PPA_source_non_coop

+

PCCT_tx +

PCCT_rx)/Rb.

(4)

where PPA_source_non_coop represents the transmission power of the source. The total energy consumption per information bit using selective decode-and-forward cooperative communication may be expressed as up erESubscriptco pBaseline qualstimesStartBinomialOrMatrixup erPSubscriptup erPup erASubSubscriptminusSubscriptsourceSubSubscriptminusSubscriptco pBaselineplusleft-parenthesi normal minusup erBup erLup erEup erRSubscriptsminuspBaselineright-parenthesi timesup erPSubscriptup erPup erASubSubscriptminusSubscriptpartnerSubSubscriptminusSubscriptco pBaselineCho seplusleft-parenthesi 2minusup erBup erLup erEup erRSubscriptsminuspBaselineright-parenthesi up erPSubscriptup erCup erCup erTSubSubscriptminusSubscript xBaselineplusleft-parenthesi 3minusup erBup erLup erEup erRSubscriptsminuspBaselineright-parenthesi up erPSubscriptup erCup erCup erTSubSubscriptminusSubscriptrxBaselineEndBinomialOrMatrixslashup erRSubscriptbBaselinecom a

(5) where PPA_source_coop and PPA_partner_coop represent the transmission power of the cooperating source and partner, respectively [12]. Finally, the energy efficiency of cooperation may be defined as the percentage total energy saving achieved by cooperating, upper E Subscript s a v i n g bar c o o p bar t o t a l Baseline equals StartFraction 1 0 0 times left-parenthesis upper E Subscript n o n bar c o o p Baseline minus upper E Subscript c o o p Baseline right-parenthesis Over upper E Subscript n o n bar c o o p Baseline EndFraction period

(6) The energy efficiency of cooperation in wireless sensor networks has been investigated in [ 10], [ 11 ], and [ 13] under a variety of assumptions; these studies have confirmed that cooperation can provide considerable energy savings, even when all significant energy overheads are taken into account. Figure 3 shows the total energy saving achieved by selection decode-and-forward cooperation as the sourcedestination separation ds-d is increased. 2 Comparing (4) and (5) it becomes apparEsaving_coop_total ent that a positive is obtained only once the reduction in the total transmission energy due to cooperative diversity is greater than the overhead of the ,

2 Optimal partner location and cooperative transmit power allocation (as discussed in Section 4) were assumed in generating this plot.

Figure 3. Total energy saving from selection decode-and-forward cooperation vs. source-destination separation. Cooperative communication becomes energy efficient beyond a threshold source-destination separation, once the circuit energy overhead of cooperation is compensated by the reduction in transmission energy due to cooperative diversity. A negative energy saving indicates that non-cooperative communication is more energy efficient, e.g. -150%means that cooperation consumes 2.5 times the energy of a non-cooperative system

increased circuit energy consumption of cooperation. Whereas circuit energy is a fixed overhead, it is evident from (3) that transmission energy is a function of transmission distance. Thus cooperation becomes energy efficient beyond a threshold source-destination separation, as illustrated by Figure 3. Figure 3 shows that the energy saving achieved by cooperation increases with increasing ds−d, as the cooperative circuit energy overhead becomes decreasingly significant. Moreover, very significant energy savings are achieved past the breakeven threshold distance. For example, cooperation can reduce the energy cost of communication by 50% for a source 16m away from the destination receiver and by 88% for a source 30m away. The energy saving curve asymptotically approaches the maximum total energy saving achievable through cooperation, which is simply given by the reduction in the total transmission energy. For the system under consideration, this maximum energy saving of 94% is effectively reached past a sourcedestination separation of 60m, as demonstrated by Figure 3. Therefore, provided the transmission range of communication is beyond a certain threshold, cooperative communication has the potential to dramatically reduce the total energy cost of wireless communication in sensor networks.

4. Practical Energy Efficiency of Cooperation in Wireless Sensor Networks Although cooperation has the potential to significantly improve the energy efficiency of wireless communication, it is important to examine to what extent such energy savings are practically achievable in a wireless sensor network. To this end, we start

this section by discussing the optimal allocation of transmission power for energy efficient cooperation for an arbitrary source and partner node pair. We then consider the energy savings achieved for a given source node cooperating with a range of potential partners using this optimal power allocation. For practical deployment of cooperative communication to be feasible in wireless sensor networks, nodes must be able to perform partner selection autonomously given a set of candidate partner nodes and allocate power for the cooperative transmission. In this section we show that large network-wide energy efficiency gains can be attained by deploying a simple and distributed cooperation protocol that nevertheless allows nodes to make near-optimal cooperation decisions.

4.1. Optimal Power Allocation and Partner Choice for Energy Efficient Cooperation The optimal allocation of transmission power to the cooperating source and its partner minimises the overall energy consumed by the cooperative system, while achieving reliable communication. Formally this may be expressed as arg times min Underscript up er E Subscript s bar t x Baseline times comma up er E Subscript p bar t x Baseline Endscripts times StartSet up er E Subscript c o o p Baseline EndSet comma subject o up er B up er E up er R Subscript c o o p Baseline les -than-or-equal-to p Subscript b Baseline times comma

(7) where Ecoop is given by (5), BERcoop is given by (1), and Es_tx and Ep_tx represent the transmit energies per information bit of the cooperating source and partner, respectively [12]. For a given source and a fixed destination, the best cooperation partner out of a set of N candidate partners is that which gives the highest total energy saving with optimal power allocation. This best partner choice problem may be expressed as arg times max Underscript up er L Subscript s minus p Sub Subscript i Subscript Baseline times comma up er L Subscript p Sub Subscript i Subscript minus d Baseline Endscripts times StartSet up er E Subscript s a v i n g bar c o o p bar t o t a l Baseline times times left-parenthesi up er L Subscript s minus p Sub Subscript i Subscript Baseline times comma up er L Subscript p Sub Subscript i Subscript minus d Baseline right-parenthesi EndSet imes comma i element-of StartSet 1 comma 2 comma period period period period times comma up er N EndSet comma

(8) where Esaving_coop_total is given by (6), Ecoop is determined by the solution of (7), and associated with the ith candidate partner node are Ls−pi and Lpi−d , the average path loss on the source-partner and partner-destination channels, respectively [12]. The optimisation problem in (7) has been shown to be non-linear, necessitating the use of a search-based method to find the optimal power allocation for energy efficient cooperation [ 12]. The total energy savings achieved from cooperation using this optimal power allocation are shown in Figure 4 for a range of potential partner locations. 3 The source node is located 25m away from the destination receiver, which is located at the origin. The energy saving contours of Figure 4 are roughly concentric circles centered midway between the source and the destination, where the energy efficiency of cooperation increases with increasing proximity of the partner to this point. The solution to the partner choice problem in (8) is evident from this

3 We illustrate partner choice in terms of network geometry by using (3) to map the path loss values Ln andaato transmission distances ds−pi and dpi−d, respectively.

Figure 4. Total energy savings for a source node 25m away from the destination receiver cooperating with a range of potential partners, using selection decode-and-forward cooperation with optimal transmit power allocation

observation: the optimal partner location is clearly midway between the source and the destination. Interestingly, the diameter of the partner choice region for a given energy efficiency of cooperation is generally greater than the source destination separation, as illustrated by Figure 4. This relatively large partner choice region is due to the adaptive nature of selection decode-and-forward and translates practically to a wide choice of partners for energy efficient cooperation. Namely, significant energy savings can be attained even if a source node cooperates with a non-ideal partner. This flexibility of cooperative communication makes it a particularly effective practical energy saving technique in randomly-deployed wireless sensor networks. Furthermore, it has been shown [12] that a particular energy efficiency of cooperation is achieved within a larger partner choice region for a larger sourcedestination separation. This implies that a source further away from the destination can seek its partner from within a greater region. In practical terms, this is highly advantageous as source nodes with the highest initial energy requirements will have the broadest choice of cooperation partner, and thus be the most likely to obtain energy savings through cooperation. 4.2. Energy Efficient Cooperation Protocol for Wireless Sensor Networks We present a simple distributed cooperation protocol for wireless sensor networks, whereby each source node autonomously makes cooperation decisions based on the simple yet near-optimally energy efficient cooperation strategy developed in [12]. Specifically, the source node firstly selects its cooperation partner given its set of N available candidate partners {(Ls−p1,Lp1−d), (Ls−p2,Lp2−d),..., (Ls−pN,LpN−d)}, based on the rule “select the partner that is located closest to the midway point between the source and destination” [12]. The source then calculates

the best transmit power allocation for the cooperative transmission with its chosen partner using StarLyout1sRowuperESubscriptsbartxBaselin times qualsStarRotSartFaction3timesuperN0squaredtimesuperLSubscript minusdBaselin uperLSubscriptsminusdBaselin Over4pSubscriptbBaselin EndFractionEdRotplusStarRotSartFactionuperKuperN0squaredtimesuperLSubscriptsminuspBaselin uperLSubscriptsminusdBaselin Over4pSubscriptbBaselin EndFractionEdRotcom a2ndRowuperESubscript bartxBaselin equalsStarStarFactionleft-parenthesi 1minusStarFactionuperKuperN0timestimesuperLSubscriptsminuspBaselin OveruperESubscriptsbartxBaselin EndFractiontimesright-parenthesi tmes3uperN0squaredtimesuperLSubscriptsminuspBaselin uperLSubscript minusdBaselin timesOverOver16timesuperESubscriptsbartxBaselin timeslft-parenthesi pSubscriptbBaselin minusStarFactionuperKuperN0squaredtimesuperLSubscriptsminuspBaselin uperLSubscriptsminusdBaselin Over4uperESubscriptsbartxSuperscipt2Baselin EndFractionright-parenthesi End Fractioncom aEndLayout

(9)

where Ls-d is the average path loss on the source-destination channel, N0 is the Gaussian noise power spectral density and K is a parameter related to BLERs-p and is dependent on the message block size and the modulation scheme [ 12]. Finally, the source calculates the energy saving expected from cooperating with its chosen partner using (6) ; if the result is positive, the source informs the selected partner node of Ep_tx; otherwise, the source simply opts for non-cooperative communication.

Therefore, the distributed coordination of cooperative communication is made feasible by employing simple heuristics that can be easily computed by resource-constrained sensor nodes based on local information. Source nodes can easily estimate Ls−d and {Ls−p1,Ls−p2,...,Ls−pN} through simple average received signal strength measurements, whereas they can obtain knowledge of {Lp1−d,Lp2−d,...,LpN−d} either via a dedicated ‘advertisement’ broadcast from available partners or during the neighbourhood discovery stage of the sensor network’s self-organisation. Moreover, since these are average channel measurements and the sensor network is assumed to be static, cooperative partner selection and power allocation does not need to be done anew message-by-message. Instead, source nodes only repeat set up of their cooperative communication in the event of a major reconfiguration of the sensor network. Cooperative communication is thus coordinated with a low signaling overhead, making this cooperation protocol particularly well suited to wireless sensor networks. In the following example we demonstrate the effectiveness of this distributed cooperation protocol, showing that large network-wide energy savings can be attained via cooperative communication without the need for central coordination. We consider a wireless sensor network consisting of a central destination receiver and 50 sensor nodes randomly uniformly placed over a circular network area with a radius of 100m. As per the above cooperation protocol, each source node selects its cooperation partner from the other 49 nodes in the network and allocates power for the cooperative transmission. The simulation results of this network wide cooperative communication are presented in Figure 5. In this simulation a very significant overall communication energy saving of 86% is attained compared to a non-cooperative network. Furthermore, as illustrated in Figure 5(a), nearly all source nodes in the network achieve a very large total cooperative energy saving of around 80% to 90%. Figure 5(a) also shows that two nodes very close to the destination choose not to employ cooperative communication, as they cannot obtain

Figure 5. Energy efficient cooperative communication in a randomly deployed wireless sensor network of 50 sensor nodes with a destination receiver at the centre; (a) size of node is proportional to the total energy saving achieved by that source node via cooperative communication (b) size of node is proportional to the number of times that node serves as a cooperation partner to other nodes in the network an

energy

saving

from

cooperating

with any other node in the network.

Despite

this, these two nodes do serve as partners for the cooperative transmissions of other source nodes, as shown in Figure 5(b) In fact, Figure 5(b) reveals that only nodes that are relatively close to the destination are selected as cooperation partners, which is a natural consequence of the implemented partner choice rule. Namely, sensor .

nodes with inherently low communication energy requirements are chosen to help nodes with high energy requirements by serving as their cooperation partners. This illustrates how effectively this simple distributed cooperation protocol facilitates a reallocation of resources among sensor nodes to improve the overall energy efficiency of the network. However, this bias towards partner nodes near the destination may in the long term have a negative impact on the network’s lifetime, as very popular partner nodes prematurely deplete their own energy supply in helping other nodes. A modified partner choice strategy may be required to address this issue,

whereby

a

limit is

placed

on

the number of times

a

node

can serve as a

cooperation

partner.

5. Conclusions In this chapter we have shown that cooperative communication can be deployed in wireless sensor networks as an effective practical energy saving technique. We have presented an energy model of cooperation to demonstrate that cooperative communication has the potential to significantly reduce the total energy cost of wireless communication, provided the transmission range is beyond a certain threshold.

We have shown that the partner choice region for energy efficient cooperation is large relative to the source-destination separation. Thus significant energy savings are attainable even if a source node cooperates with a non-ideal partner. This flexibility is due to the adaptive nature of the selection decode-and-forward cooperative diversity scheme, and makes cooperation a particularly effective energy saving technique in randomly-deployed wireless sensor networks. We have also shown that a source node with high initial communication energy requirements is more likely to obtain energy savings through cooperation, as it can seek its partner from within a greater region. We have presented a simple distributed cooperation protocol for wireless sensor networks, whereby each source node autonomously makes cooperation decisions based on a simple yet near-optimally energy efficient cooperation strategy. Cooperative communication is coordinated with a low signaling overhead within this protocol, making it particularly well suited to wireless sensor networks. We have demonstrated the effectiveness of this cooperation protocol through an example, showing that large network-wide energy savings can be attained via cooperative communication without the need for central coordination.

Acknowledgements Ljiljana Simić is supported by the Bright Future Top Achiever Doctoral Scholarship (Tertiary Education Commission, New Zealand).

References [1] H. Karl and A. Willig, Protocols and Architectures for Wireless Sensor Networks. Hoboken, NJ: John Wiley and Sons, 2005. [2] I. F. Akyldiz, S. Weilian, Y. Sankarasubramaniam, and E. Cayirci, “A survey on sensor networks” IEEE Communications Magazine, vol. 40, no. 8, pp. 102–114, August 2002. [3] V. Raghunathan, C. Schurgers, P. Sung, and M. B. Srivastava, “Energy-aware wireless microsensor networks,” IEEE Signal Processing Magazine, vol. 19, no. 2, pp. 40–50, March 2002. [4] T. S. Rappaport, Wireless communications: principles and practice, second ed. Upper Saddle River: Prentice Hall PTR , 2002. [5] B. Vucetic and J. Yuan, Space-Time Coding, Chichester: Wiley, 2003. [6] A. Sendonaris, E. Erkip , and B. Aazhang, “User cooperation diversity. Part I: System description,” IEEE Transactions on Communications, vol. 51, no. 11, pp. 1927–1938, November 2003. [7]— , “User cooperation diversity. Part II: Implementation aspects and performance analysis,” IEEE Transactions on Communications, vol. 51, no. 11, pp. 1939–1948, November 2003. [8] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversity in wireless networks: Efficient protocols and outage behavior,” IEEE Transactions on Information Theory, vol. 50, no. 12, pp. 3062–3080, December 2004. [9] T. E. Hunter and A. Nosratinia , “Diversity through coded cooperation,” IEEE Transactions on Wireless Communications, vol. 5, no. 2, pp. 283–289, February 2006. [10] S. Cui, A. J. Goldsmith, and A. Bahai, “Energy-efficiency of MIMO and cooperative MIMO techniques in sensor networks,” IEEE Journal on Selected Areas in Communications, vol. 22, no. 6, pp. 1089–1098, August 2004.

“

S. M. Berber and K. W. Sowerby Energy-efficiency of cooperative diversity techniques in wireless sensor networks,” in Proceedings of18th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC'07) Athens , 2007 S. M. Berber and K. W. Sowerby Partner choice and power allocation for energy [12] Lj. efficient cooperation in wireless sensor networks ,” submitted to IEEE International Conference on Communications (ICC 2008) Beijing 2008 [13] S. K. Jayaweera Virtual MIMO-based cooperative communication for energy-constrained wireless sensor networks ,” IEEE Transactions on Wireless Communications vol. 5 no. 5 pp. 984 989

[11] Lj. Simić

Simić

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May 2006

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Cross-Layer Optimization with Guaranteed QoS for Wireless Multiuser OFDM Systems Nan Zhoua , XuZhua,1 and Yi Huanga a University of Liverpool, United Kingdom Abstract. We propose a novel cross-layer optimization scheme for the downlink multiuser orthogonal frequency division multiplexing (OFDM) system. The proposed maximum weighted capacity (MWC) based resource allocation at the physical (PHY) layer can provide a much better QoS than the previous resource allocation schemes, while maintaining the highest or nearly highest capacity and costing a similar complexity. In particular, the more fluctuation in different users’ data arrival rates, the more advantages of MWC in both QoS and capacity. Besides, our proposed delay satisfaction (DS) scheduling at the medium access control (MAC) layer allows more than one connection to be served in each slot, which is more efficient than conventional scheduling. Keywords: Wireless Telecommunications, 4G, Resource allocation, Scheduling.

1. Introduction The instructions should provide you with all the information required to comply with the RIVER Publishers submission standards. The official language of all book chapters is English. Use a British English spell-checker, if possible. Values should be in SI units. In traditional network architectures, each layer is designed to operate independently [1], which however does not utilize the spectrum and energy efficiently. Cross-layer optimization [1][2], which contains dynamic behaviors based on integrated adaptive design across different layers, has been proposed to optimize the system performance. Resource allocation and management with cross-layer optimization play a particularly crucial role in wireless networks which are confronted with time-varying fading channels, limited bandwidth and competition of air resources among multiple users [3][4]. Orthogonal frequency division multiplexing (OFDM) [ 10] is effective to combat frequency-selective channels and to support high data rate services, which has been adopted in wireless LANs (IEEE 802.11 a & 11g), WiMAX (IEEE 802.16) and 3GPP LTE downlink systems [ 6]. Much research work has been carried out on dynamic

1

Corresponding Author: Xu Zhu, Department of Electrical Engineering and Electronics, The University Liverpool, L69 3GJ, UK. Email: [email protected]

of Liverpool,

DOI: 10.1201/9781003336853-11

Cross-Layer Optimization with Guaranteed QoS

subcarrier and power allocation to different OFDM users, which allows a flexible multiuser access and enhancement of the multiuser diversity. In [5], each subcarrier is allocated to the user with the best channel gain on that subcarrier, and the power allocation is based on water-filling. In [7], a so-called proportional fairness (PF) scheme was proposed for resource allocation to guarantee the fairness among users with proportional fairness coefficients employed. However, the work in [5] and [7] was only based on maximizing the total capacity. In wireless networking, the quality of service (QoS) plays a crucial part in performance measurement. For example, the response time for webpage browsing is user sensitive [3]. Therefore, cross-layer optimization to meet the required QoS is desirable [10]. Joint channel-aware and queue-aware data scheduling was proposed in [8] and [9], which however was based on a single carrier system. The utility based resource allocation and scheduling were proposed in [1] and [3]. However, they assumed that each user has only one connection, which is not practical. In this paper, we propose a novel cross-layer optimization scheme with guaranteed QoS for the downlink multiuser OFDM system, which includes a so-called maximum weighted capacity (MWC) based resource allocation and a delay satisfaction (DS) based scheduling. Our work is different in that we perform joint channel-aware and queue-aware resource allocation at the physical (PHY) layer, using the QoS information obtained from scheduling at the medium access control (MAC) layer. The MAC layer utilizes the resource allocation results for data management. We also allow each user to have more than one connection. Simulation results show that with different distributions of users’ data arrival rates, the MWC based resource allocation can provide a much better QoS than the MC [5] and PF [7] based resource allocation schemes, while maintaining the highest or nearly highest system capacity and costing a similar complexity. Besides, our proposed DS based scheduling is more efficient than conventional scheduling, allowing more than one connection to be served in each slot. In Section II, we present the system model. The MWC based resource allocation of the PHY layer and the DS based data scheduling of the MAC layer are presented in Sections III and IV, respectively. Simulation results are shown Section V, and the conclusion is drawn in Section VI.

2. Typographical Style and General Layout We consider an OFDM system with K users as shown in Figure 1 to meet the QoS requirements. Without loss of generality and for simplicity, we assume that each subcarrier is occupied by only one user [5,7]. This work can be easily extended to the case where each subcarrier can be shared by more than one user. In this system, the subcarrier and power controller at the PHY layer performs subcarrier and power allocation, and the traffic controller at the MAC layer performs data scheduling, respectively. The traffic controller transfers the QoS information of users to the ,

3. Typographical Style and General Layout

Figure 1. Multiuser OFDM System

subcarrier and power controller for the purpose of resource allocation, and the resource allocation result is fed back to the traffic controller in the base station for scheduling of the data to be sent out in each slot. We assume a total bandwidth of B shared by N subcarriers. Let Ωk denote the 1, index set of subcarriers allocated to user k (k ....,K). Let pk,n be the power allocated to user k on subcarrier n ∈ Ωk, hk,n the corresponding channel gain, and N0 the power spectral density of additive white Gaussian noise (AWGN). Assuming perfect channel estimation, the achievable data rate of user k on subcarrier n is =

expressed

as: up er R Subscript k comma n Baseline equals StartFraction up er B Over up er N EndFraction log Subscript 2 Baseline times left-parenthesis 1 plus p Subscript k comma n Baseline gamma Subscript k comma n Baseline right-parenthesis

(1) where γk,n =|hk,n|2/(N0B/N) is the channel-to-noise power ratio for user k on subcarrier n. Therefore, the total data rate of user k is given by: up er R Subscript k Baseline quals normal up er Sigma Underscript n el ment-of normal up er Omega Subscript k Baseline Endscripts up er R Subscript k com a n Baseline times

(2)

3. Typographical Style and General Layout In this section, we first review the MC [5] and PF [7] based resource allocation schemes, and then propose a MWC based resource allocation. 3.1. Maximum Capacity Based Resource Allocation The resource allocation scheme in [5] is to maximize the system throughput, i.e., to maximize up er J equals times normal up er Sigma Underscript k equals 1 Overscript up er K Endscripts up er R Subscript k Baseline

(3)

subject d to

. .,N}, where PTOTAL denotes the total power. The optimal solution for (3) contains two steps | 5J. The first step is to allocate each subcarrier to the user with the best channel gain on that subcarrier, and the second step is to perform the water-filling power allocation to each subcarrier. However, the system capacity can not be maximized by this algorithm unless all users have adequate data to send. In practice, the MC based scheme may lead to the case where the users occupying air resources do not have a high demand for resources, while other users with urgent traffic demands are not allocated enough resources due to poor channel gains. Furthermore, the MC based scheme assumes that the data are not delay sensitive, which is not practical. Therefore, the MC scheme is not effective to guarantee the throughput, fairness and QoS. ΩK d {1, 2,

3.2. Proportional Fairness Based Resource Allocation Different from the MC based scheme in Section III-A, the proportional fairness (PF) based scheme [7] takes the fairness into account for resource allocation, which is to maximize (3) subject to the conditions following (4) and an additional constraint below: R1

:

R2

:

...

:

RK

=

η1 :

η2

:...:ηK(4)

where ηk(k = 1,...,K) are a set of predetermined ratio values to guarantee the proportional fairness among users. In this paper, we assume that all users have equal data rates, i.e., ηk = 1 (k = 1,...,K). From (3) and (4) it can be deduced that the PF scheme guarantees the fairness at the cost of system capacity. It is shown in [7] that PF guarantees the resource allocation to all users even if a particular user has a much better channel gain than other users. However, PF does not consider the QoS information, e.g., the queuing delay [10]. 3.3. Maximum Weighted Capacity Based Resource Allocation We propose a resource allocation scheme to maximize the weighted sum of all users’ capacity, i.e., to maximize up er J equals normal up er Sigma Underscript k equals 1 Overscript up er K Endscripts up er W Subscript k Baseline up er R Subscript k

(5) where Wk denotes the weight for user k which indicates the QoS information for user k, and is obtained from the result of data scheduling at the MAC layer as described in Section IV-B. The conditions following (3) apply.

It is difficult to optimize subcarrier and power allocation at the same time, especially in a real-time system. Hence, we separate the solution into two steps — subcarrier allocation and power allocation.

Optimal MWC based subcarrier allocation:

For simplicity, we assume uniform all subcarriers, i.e., each subcarrier is allocated a power p PTOTAL/N. Optimal subcarrier allocation leads to the maximum cost function, which is denoted by Jmax. If an arbitrary subcarrier n allocated to user k (k . . , 1, K) with optimal subcarrier allocation is now reassigned to user j, let J' denote the resulting cost function. The difference between the two cost functions is power allocation

across

=

=

given by:

Jmax

-

J'

=

WkRk,n

-

WjRj,n ≥ 0(6)

Substituting (1) into (6), we have StarFactionup erWSubscriptkBaselineOverup erWSubscriptjBaselineEndFractiongreater-than-orequal-toStarFactionlogSubscript2Baselinetimesleft-parenthesi 1pluspgam aSubscriptjcom anBaselineright-parenthesi OverlogSubscript2Baselinetimesleft-parenthesi 1pluspgam aSubscriptkcom anBaselineright-parenthesi EndFraction

(7) which implies that with optimal subcarrier allocation, subcarrier n should be allocated to user k rather than user j if (7) is satisfied. However, it is prohibitively complex to perform optimal subcarrier allocation with a large number of subcarriers. Therefore, a suboptimal scheme is desired. Suboptimal MWC based subcarrier allocation: Intuitively, to maximize the cost function in ( 5), a larger weight demands a higher data rate. Letting Rk/Wk denote the rate-to-weight ratio (RWR) and assuming uniform power allocation across all subcarriers, we employ the following suboptimal subcarrier allocation scheme, where the user with the lowest RWR is allowed to pick subcarriers in each iteration: 1)

Initialization: Ø for all k (k 0, Ωk 1, K), sort Wk in the descenda) Set Rk . . N} denote the set of unallocated {1, 2, ing order, and let L 1 to K: subcarriers. For k b) If γk,m ≥ ηk,n, assign subcarrier m to user k, i.e., add subcarrier m to Ωk. Remove subcarrier m from L. Update Rk according to (2) Find the minimum Rk/Wk (k =1,.K)repeat 1-b) for the corresponding , user k. Ø. Repeat 2) until L =

=

=

. . .

=

=

.

2) 3)

=

The proposed suboptimal MWC based subcarrier allocation requires a complexity of O(KN), similar to the complexities of MC [5] and PF [7]. In a special case with equal data rates and equal weights, i.e., R1 = R2 = ... = RK and W1 = W2 = ... = WK, the suboptimal MWC based subcarrier allocation reduces to the PF based subcarrier allocation. Optimal MWC based power allocation: Following subcarrier allocation, the optimal power allocation for each user can be obtained by using the Lagrange multiplier, i.e., (5) can be rewritten as: up erJequalsnormalup erSigmaUnderscriptkequals1Overscriptup erKEndscriptsup erWSubscriptkBaselineup erRSubscriptkBaselinepluslamdatimesleft-parenthesi normalup erSigmaUnderscriptkequals1Overscriptup erKEndscriptsnormalup erSigmaUnderscriptnel ment-ofnormalup erOmegaSubscriptkBaselinetimesUnderUnderscript imesEndscriptspSubscriptkcom anBaselineminusup erPSubscriptup erTup erOup erTup erAup erLBaselineright-parenthesi

(8)

Subject optimal

tod

pk,n

solution for pk,n is

=

PTOTAL and pk,n

>

0.

Letting ∂J/∂pk,n

0, the

=

given by:

pSubscriptkcom anBaseline qualsmaxleft-braceStartFractionup erWSubscriptkBaselineOversigma-sum ationUnderscriptiequals1Overscriptup erKEndscriptsleft-parenthesi up erWSubscriptiBaselineSubscriptBaselinetimes izeofleft-parenthesi normalup erOmegaSubscriptiBaselineSubscriptBaselineright-parenthesi right-parenthesi EndFractionleft-parenthesi up erPSubscriptup erTup erOup erTup erAup erLBaselineplusnormalup erSigmaUnderscriptiequals1Overscriptup erKEndscriptsnormalup erSigmaUnderscriptqel ment-ofnormalup erOmegaSubscriptjBaselinetimesEndscriptsStartFraction1Overgam aSubscripticom aqBaselineEndFractionright-parenthesi minusStartFraction1Overgam aSubscriptkcom anBaselineEndFractioncom a0right-braceperiod

(9)

Consider

=

and j and k (j, k ∈{..,K}1), and subcarriers m ∈Ωj subcarriers allocated to users j and k, respectively. By can derive:

users

arbitrary ∂J/∂pj,m 0, we

are two

n

∈ Ωk = ∂J/∂pk,n

StarFactionup erWSubscriptjBaselineOverup erWSubscriptkBaselineEndFractionequalsStarFactiongam aSubscriptkcom anBaselinetimesleft-parenthesi 1pluspSubscriptjcom amBaselinetimesgam aSubscriptjcom amBaselineright-parenthesi Overgam aSubscriptjcom amtimesBaselinel ft-parenthesi 1pluspSubscriptkcom anBaselinetimesgam aSubscriptkcom anBaselineright-parenthesi EndFraction

(10) • If Wj/Wk = 1, from (10) it can be derived that p Subscript j comma m Baseline minus p Subscript k comma n Baseline equals StartFraction gamma Subscript j comma m Baseline minus gamma Subscript k comma n Baseline Over gamma Subscript j comma m Baseline gamma Subscript k comma n Baseline EndFraction

(11) (11) implies that with equal weight, the subcarrier with a better channel gain is allocated more power, which is the same result as water-filling [11]. • If Wj/Wk > 1, we have p Subscript j com a m Baseline minus p Subscript k com a n Baseline greater-than StartFraction gam a Subscript j com a m Baseline minus gam a Subscript k com a n Baseline Over gam a Subscript j com a m Baseline times gam a Subscript k com a n Baseline EndFraction

(12) (12) implies that the subcarrier corresponding to the user with a higher weight is allocated more power than the case using water-filling.

4. Delay Satisfaction Based Data Scheduling 4.1. DS Based Data Scheduling After receiving the resource allocation results from the PHY layer, which indicates the amount of data allowed for each user, the MAC layer performs scheduling for each batch of data to be sent out. We propose a scheduling scheme, which assigns a higher weight to the batch of data packets with a less DS, i.e., the data with the least DS should be sent out first. We define a DS indicator Ck,i,l for the batch of packets for connection i of user k, which arrive in slot l (l ∈ [Lc Lm, Lc ]). where Lc denotes the current slot, and Lm is the delay bound for the ith connection, which is the class-m QoS traffic, in terms of slot. Also let Gm be the guard slot of the class-m QoS traffic, and Sk,i,l be the waiting time for connection i of user k, which is the duration between slot l and —

the current slot. The DS indicator Ck,i,l is expressed as Ck,i,l = Lm − Gm − Sk,i,l which implies that the longer the data’s waiting time is, the less the DS is. Let Uk,i,l denote the weight of the batch corresponding to connection i of user k arriving in slot l, which is given by: up erUSubscriptkcom aicom alBaseline qualsStartLayoutEnlargedleft-brace1stRow left-bracketbetaSubscriptmBaselineslashleft-parenthesi up erCSubscriptkcom aicom alBaselineplus1right-parenthesi right-bracketlogleft-parenthesi up erDSubscriptkcom aicom alBaselineplus1right-parenthesi timesleft-parenthesi up erCSubscriptkcom aicom alBaselinegreater-than0right-parenthesi 2ndRow betaSubscriptmBaselinetimeslogleft-parenthesi up erDSubscriptkcom aicom alBaselineplus1right-parenthesi timesleft-parenthesi minusup erGSubscriptmBaselineles -than-or-equal-toup erCSubscriptkcom aicom alBaselineles -than-or-equal-to0right-parenthesi EndLayout imes

(13) where βm is the class-m QoS coefficient, and Dk,i,l is the amount of data of connection i arriving in slot l. The proposed DS based scheme performs scheduling by descending order of the weights obtained in (13) which implies that the batches of all connections which will become time out very soon are given a higher priority to be sent out. In conventional scheduling [8 ][ 9], where only one connection is served in each slot until either all the PHY layer resources are consumed or the buffer is empty. However, this is not efficient if the data of other connections are more urgent than the currently served data. Therefore, our proposed DS based scheduling is more efficient, which allows ,

the most urgent data to be sent out first.

4.2. Weight Calculation for MWC based Resource Allocation To guarantee the QoS, it is desirable that the resource allocation at the PHY layer acquires the channel information for each user and employs the QoS information obtained at the MAC layer, including the queue length, the QoS class of queues, and the waiting time of queues. As the weight Uk,i,l given by (13) contains the above QoS information, the weights in (5) for the MWC based resource allocation are determined by adding the weights of all valid batches of connections for each user: up erWSubscriptkBaseline qualsnormalup erSigmaUnderscriptiEndscripts imesnormalup erSigmaUnderscriptlequalsup erLSubscripticom asBaselineOverscriptup erLSubscripticom aeBaselineEndscriptsup erUSubscriptkcom aicom alBaselinetimes

(14) where Li,s and Li,e denote the arrival and time out slots for connection i,

respectively.

5. Simulation Results We use simulation results to show performance of the proposed cross-layer optimization scheme, in terms of the system bandwidth efficiency and the delay outage probability. Letting ξk,i(l) denote the delay outage probability of the real time traffic for connection i of user k in slot l, the delay outage probability in slot (l + 1) is calculated over a window size of d = 1000, given by: xiSubscriptkcom aitmesBaselineleft-parenthesi lplus1right-parenthesi equalsStartLayoutEnlargedleft-brace1stRow xiSubscriptkcom aiBaselinetimesleft-parenthesi lright-parenthesi timesleft-parenthesi 1minus1slashphirght-parenthesi plus1slashphitmesleft-parenthesi up erS ubscriptkcom aicom amaxBaselinegreater-than-or-equal-toup erLSubscriptmBaselineright-parenthesi 2ndRow xiSubscriptkcom aiBaselinetimesleft-parenthesi lright-parenthesi timesleft-parenthesi 1minus1slashphirght-parenthesi timesleft-parenthesi sSubscriptkcom aicom amaxles -thanup erLSubSubscriptmSubscriptright-parenthesi BaselineEndLayout

(15)

Figure 2. System capacity with uniformly distributed data arrival rates where Sk,i,max is the head-of-line delay of the fitt connection for user k. We employ the proposed MWC based resource allocation at the PHY layer in comparison with MC [ 5 ] and PF [ 7], and the DS based scheduling at the MAC layer for consistency. An equal data rate condition is applied for PF, i.e., R1 RK. We R2 consider a system with K 8 users, a total transmit power of PTOTAL 1W, 1MHz which is divided into N 64 subcarriers. and a total bandwidth of B =

=

...

=

=

=

=

=

The channel has six independent Rayleigh fading paths with an exponentially delay 80 dBW/Hz. The system slot profile. The power spectral density of AWGN is N0 is set to be 1ms for simplicity. In our simulations, each user has two types of streams 5 and the of the conversational class (real time) with a QoS-class coefficient βm interactive class (non real time) with βm 3, respectively, as in UMTS [ 12]. The maximum transfer delays for the conversational and interactive classes are 30ms and 500ms, respectively. It is assumed that the arrival process of the conversational class stream is Poisson distributed, and the interactive class streams are always available, which is a reasonable assumption for applications such as File Transfer Protocol (FTP). —

=

=

=

Figures 2 and 3 demonstrate performance of MWC, compared to MC and PF, with uniformly distributed data arrival rates for all users. All the resource allocation schemes achieve the same capacity when the total data arrival rate is below 7 Mbps. At a higher data arrival rate, the maximum capacity achieved by MWC is only 0.7 bps/Hz less than the maximum capacity achieved by MC. In this case, the weight Wk in (5) is approximately equal for all users since their data arrival rates are approximately equal. Therefore, MWC should provide a close performance to MC. The marginal capacity loss of MWC over MC is due to the suboptimal subcarrier allocation as described in Section III-C, while the complexity of MWC is

Figure 3. Delay outage probability of the conversational class stream with uniformly distributed data arrival rates

similar to that of MC. According to [9], the acceptable delay outage probability of the conversational class is below 5%. Figure 3 shows that MWC still provides a satisfactory QoS even with a high data arrival rate of 20 Mbps, while MC can only provide a good QoS when the data arrival rate is below 10 Mbps. Therefore, it can be deduced that with uniformly distributed data arrival rates for all users and a high total data arrival rate (e.g., above 7 Mbps), MWC provides a better QoS than MC while maintaining a comparable capacity. With approximately equal data rates and equal weights, MWC also has a close performance to PF with an equal data rate condition applied for PF, as discussed in Section III-C. Figures 4 and 5 demonstrate performance of MWC, MC and PF, when the QoS streams of different users have exponentially distributed data arrival rates, as shown in Table 1. Compared to the case with uniformly distributed data rates shown by Figure 2 MWC suffers from little capacity loss (less than 0.4bps/Hz) at a higher ,

total data arrival rate, while MC and PF are sensitive to the distribution of users' data rates. Figure 4 shows that by utilizing the QoS information, MWC achieves a significant capacity gain of up to 72% over MC and PF, when the total data arrival rate is between 5 Mbps and 25 Mbps. Note that in the ideal case where all users have adequate data to send out (e.g., with uniformly distributed data rates), MC should achieve the highest capacity. However, this can not be satisfied if the data arrival rates of all users are exponentially distributed. Figure 5 shows that MWC also significantly outperforms MC and PF in terms of the delay outage probability. MWC achieves a delay outage probability below 5% when the data arrival rate is around 13 Mbps, while MC and PF can only provide such a good QoS when the data arrival rate is below 6 Mbps and 5 Mbps, respectively.

Figure 4. System capacity with exponentially distributed data arrival rates

Figure 5. Delay Outage Probability of the conversational class stream with exponentially distributed data arrival rates

Table 1. 1. Average data data arrival arrival rate rate of of each each user user with with a a system total total Table data arrival rate of data arrival rate of Q Mbps

Throughput for User ID 1 2 3 4 5

6 7

the Conversational Class Streams

0.46Q 4.22Q 4.87Q 7.72Q 21.8Q 29.76Q 66.23Q 150.66Q

Throughput for the Interactive Class Streams

1.14Q 10.54Q 12.19Q 19.3Q 54.48Q 74.4Q 165.58Q 376.65Q

6. Conclusion We have proposed a cross-layer resource allocation and scheduling scheme in the downlink multiuser OFDM system. Utilizing the QoS information obtained from scheduling, the MWC based resource allocation provides a much better QoS than MC [5] and PF [7] at a high total data arrival rate, while maintaining the (nearly) highest system capacity and costing a similar complexity. The capacity achieved by MWC is robust to the distribution of all users’ data arrival rates. In particular, the more fluctuation in different users’ data arrival rates, the more advantages of MWC over MC and PF in both QoS and capacity.

References [1] G. C. Song and Y. Li, “Utility-based resource allocation and scheduling in OFDM-based wireless broadband networks,” IEEE Community Magazine, vol. 43, pp. 127–134, December 2005. [2] J. Chen, T. Lv, and H. Zheng, “Joint cross-layer design for wireless QoS content delivery,” in Proceedings of IEEE ICC ’04, vol. 7, pp. 4243–4247, June 2004. [3] G. C. Song, Y. Li, L. J. Cimini , Jr., and H. T. Zheng, “Joint channel-aware and queue-aware data scheduling in multiple shared wireless channels,” in Proceedings of IEEE WCNC ’04, vol. 3, pp. 1939–1944, March 2004. [4] R. A. Berry and E.M. Yeh, “Cross-layer wireless resource allocation,” IEEE Signal Processing Magazine, vol. 21, pp. 59–68, September 2004. [5] J. Jang and K. B. Lee, “Transmit power adaptation for multiuser OFDM systems,” IEEE JSAC, vol. 21, pp. 171–178, February 2003. [6] H. G. Myung, “Single carrier orthogonal multiple access technique for broadband wireless communications,” PhD Dissertation, Polytechnic University, Brooklyn, NY, January 2007. [7] Z. Shen, J. G. Andrews, and B. L. Evans, “Adaptive resource allocation in multiuser OFDM systems with proportional rate constraints,” IEEE Transactions on Wireless Communication, vol. 4, pp. 2726 –2737, November 2005. [8] M. Andrews, K. Kumaran, K. Ramanan, A. Stolyar, P. Whiting , and R. Vijayakumar, “Providing quality of service over a shared wireless link ,” IEEE Communication Magazine, vol. 39, pp. 150–154, February 2001.

[9] Q. W. Liu, X. Wang, and G. B. Giannakis, “A cross-layer scheduling algorithm with QoS support in wireless networks,” IEEE Transactions on Vehicle Technology, vol. 55, pp. 839–847, May 2006. [10] C. Anton-Haro, P. Svedman, M. Bengtsson, A. Alexiou and A. Gameiro, “Cross-Layer scheduling for multi-user MIMO systems,” IEEE Communication Magazine, vol. 44, pp. 39– 45, September 2006. [11] T. M. Cover and J. A. Thomas, Elements of Information Theory. New York : Wiley, 1991. [12] 3GPP TS 23.107 V5.12.0: ftp://ftp.3gpp.org/specs/2004-03/Rel-5/23_series.

Handover Handling Issues in DVB-H Systems Giuseppe Aranitia,1, Antonio Ieraa , Antonella Molinaroa a ARTS Laboratory – Department DIMET University “Mediterranea” of Reggio Calabria-Reggio Calabria, ITALY Abstract. This chapter addresses the main issues related to handover handling in DVB-H systems. It is widely known that the DVB-H standard has been specifically conceived to deliver broadcasting content in a system characterized by a cellular coverage structure. like in traditional radio mobile systems, handover management is a critical a handover event implies the change of Transport Stream and frequency while still continuing to receive IP streams during the roaming of the receiver across DVB-H cells. The typical one-way nature of the system under study and the inherent stringent constraints of the radio mobile environment makes the procedure harsh to design. Main parameters, which need to be kept under control are: the occurrence of unnecessary handover

Accordingly,

issue to face. In DVB-H

in conditions in which the procedure is not actually required (due to ping-pong effect, for example), the power consumption at the terminal during the handover decision phase, the loss of data during the handover execution phase. In this chapter we start from a brief

events

descriptions of main feature characterizing the DVB-H standard at the Physical and Data Link layers and then we give an overview of some of the most relevant proposal of handover handling algorithms and procedures. From our brief overview it clearly emerges that several issues relevant to handover management are still open, such as, for example, the choice of the measurement parameter used during the decision phase. Pros and contras of each alternative proposal are analyzed and, eventually, some hints are given in the view of the introduction of novel features, such

as

parameters estimation and active handoff.

1. Introduction In the last few years, the introduction of digital TV and the growing deployment of broadcasting systems have enabled both the introduction of novel technological standards addressing television broadcasting and the launch of innovative multimedia and interactive services. In 1993, a European project, named “Digital video Broadcasting” (DVB), took its first steps in the view of harmonizing the different strategies, protocols, and technologies concerning the transmission of digital video signals [1]. The first valuable result is represented by the definition of DVB-S (DVB via Satellite) standard specifications. Currently, DVB-S is the standard widely adopted for television program broadcasting via satellite. Further specifications concern the distribution of the digital video signal through cable networks (DVB-C) and

1 Corresponding Author: Giuseppe Araniti, DIMET Department, University “Mediterranea” of Reggio Calabria, Via Graziella Loc. Feo di Vito — Reggio Calabria, Italy. E-mail: [email protected]. URL address: http://www.arts.unirc.it.

DOI: 10.1201/9781003336853-12

Handover Handling Issues in DVB-H Systems

by means of widespread terrestrial traditional TV infrastructures (DVB-T) [2]. This latter has gained a significant accomplishment thanks to its advantages with respect to the pre-existing analogical technology. In particular, for the same amount of RF bandwidth, DVB-T, compared to traditional TV, allows for a higher number of useful channels, a lower transmission power to cover the same distances, and a better overall quality of the video stream. Mentioned advantages have attracted the attention of mobile telephony operators, which realized that DVB technology might also be adopted to deliver new broadcast services to mobile portable receivers. A first obstacle to the accomplishment of this vision is the consideration that DVB-T can only be implemented into mobile receivers with sufficient power supply, such as vehicular terminals or laptops. Although the continuous progress in chip design technology has carried to a significant reduction in the power consumption of mobile terminals, it is unlikely that cellular telephones can ever be able to support DVB-T transmission with viable battery duration. This is the reason why a novel standard, namely the Digital Video Broadcasting-Handheld (DVB-H) [3–4] has been introduced as an evolution of DVB-T. Unlike its antecedent standards, DVB-H is not a stand-alone standard, but shares the same modulation techniques with DVB-T (Orthogonal Frequency Division Multiplexing — OFDM) [2] operating at the same frequency (III and IV UHF band, from 478 up to 518 MHz and from 806 up to 854 MHz; III VHF band with channels that goes from 174 MHz up to 189 MHz and others occupying the range of frequencies from 191MHz up to 230 MHz) with the aim of making use of the same network infrastructures. Anyway, DVB-H must allow the reception of the digital television services on handled terminals, such as new generation mobile and palmtops, characterized by low weight and limited battery power supply. Therefore, it has been crucial to add functionalities able to assure a lower battery power consumption and a higher robustness of the signal, with respect to DVB-T, due to the terminal mobility. Finally, DVB-H was also introduced to obtain a higher synergy with the Internet; thus, modifications to the protocol stack have been implemented to provide such an additional feature.

In the following section, general features of the DVB-H standard are outlined, mainly focusing on the novelties introduced by the standard: time slicing, MultiProtocol Encapsulation — Forward Error Correction (MPE-FEC), and so on. In section III considerations about the handover management procedure in a DVB-H network are addressed by pointing out points of strength and open issues. In conclusion, a brief overview is given of ongoing research activities aiming at improving the performance of the DVB-H system during handover.

2. DVB-H Features With the purpose of managing user mobility in wireless environment, DVB-H introduces, at the data link and physical layers, new features with respect to the previous DVB-T standard. The DVB-H protocol stack is reported in Figure 1.

2. DVB-H Features

Figure 1. DVB-H Protocol Stack

2.1. Physical Layer features in DVB-H general, at the physical layer, digital modulation schemes adopted by DVB in Satellite (DVB-S), cable (DVB-C), and terrestrial (DVB-T/H) systems quite differ from one another, because they have to adapt to the propagation nature of the different RF channels.. Hence, single carrier QPSK modulation is suitable to a non-linear, bandwidth unconstrained and power constrained satellite channel, while single carrier M-QAM is more suitable to bandwidth constrained and power unconstrained cable channels. As for terrestrial (both fixed and mobile wireless) channels, the presence of multi-path fading phenomena prevent form exploiting single carrier modulation techniques; therefore OFDM ( Orthogonal Frequency Division Multiplexing) modulation has been chosen |2|. DVB-H novelties at the physical layer consist in the introduction of four additional elements: (i) 4K mode orthogonal frequency division multiplexing (OFDM),, In

(ii) in-depth interleaver, (iii) Transmitter Parameter Signalling (TPS), (iv)

5 MHz

channel bandwidth. 4K mode carries out the transmission of DVB-H signal on 4096 (which the name 4K derives from) carriers by adopting OFDM. 4K mode represents a compromise solution between the 2K and 8K adopted in DVB-T standard [ 5 ], this allowing to double the transmission distance in Single-Frequency Networks (SFNs) compared to the 2K mode. Furthermore, with respect to 8K mode, it provides a good Doppler tolerance in case of mobile reception [ 6]. This implies an additional flexibility in Single Frequency Networks (SFNs) planning and provides an enhanced channel able to allow

high-speed reception [ 5 ]. To improve the performance, an in-dept interleaver is added to 4K mode, to interleave the bits over two OFDM symbols, instead of over one symbol as foreseen by native OFDM. This approach increases the tolerance to impulse noise (obtaining a performance similar to that one achievable with the 8K) and improves the robustness in mobile environment. DVB-H uses an extension of Transmission Parameter Signalling (TPS) [7] respect to the DVB-T Standard. In particular, it delivers additional information regarding: (i) the presence of DVB-H services, (ii) the possible use of MPE-FEC protection, (iii) physical transmission modes and, finally, (iv) the cell identifier. The last one is a very important feature in mobility condition, as it simplifies the service discovery procedure in neighboring cells.

Finally, at the DVB-H physical layer an additional channel bandwidth of 5 MHz has been introduced with respect to the DVB-T standard (that normally uses three different VHF/UHF bandwidths: 6MHz, 7MHz, 8MHz). 2.2. II.B Data Link Layer features in DVB-H At the data link layer of the DVB standard, IP datagrams are embedded into the MPEG-2 Transport Stream (TS) by means of Multi-Protocol Encapsulation (MPE). In particular, by using a MPE each IP datagram is encapsulated into one MPE section. A stream of MPE sections is carried into an Elementary Stream (ES) and each ES is split into packets named PES (Packetized Elementary Stream). Finally, by multiplexing more than one PES, a TS is obtained. Each TS conveys data relevant to the programs transmitted by a given broadcaster [ 5 ].

To the aim of supporting receiver mobility and reducing user terminal power consumption, the main additional elements introduced by DVB-H in the data link layer are: (i) additional Forward Error Correction for Multi Protocol Encapsulation (MPE-FEC); (ii) new signalling table inside the PSI/SI (Program Specific Information/Service Information), (iii) Time Slicing. The additional FEC-MPE module, introduced by DVB-H standard, complements the physical layer error correction by allowing to increase the S/N for reception by a handheld device. Moreover, it allows to improve the Doppler performance and the tolerance to impulse interference [ 6]. The PSI/SI Information [8–9] are the signalling tables used by DVB for service discovery into the Transport Stream. DVB-H upgrades these tables by including a new sub-set of PSI/SI parameters. These parameters provide essential information for enabling handover. The main handover parameters utilized during the handover procedures are included in the following PSI/SI tables: Network Information Table (NIT), Program Association Table (PAT), Program Map Table (PMT) [4], and IP/MAC Notification Table (INT) [10]. Time Slicing is introduced into DVB-H to reduce the terminal power consumption and to allow seamless handover. Power saving is obtained because a given program of interest for the user occupies only a fraction of the total MPEG-2 TS; as a consequence, the receiver can demodulate and decode only the portion of interest, and not the whole MPEG-2 TS. Based on this idea, Time Slicing [4] introduces a bursty data transmission (different from continuous transmissions of DVB-T) that allows the receiver to be completely powered-off during inactive periods, named off-time periods (please refer to Figure 2). Control signals are used to wake-up the receiver when the requested program is transmitted. The user does not become aware of anything related to this procedure, since the buffered data is played continuously. In [11] it was estimated that time slicing significantly reduces the average power consumption in the receiver, up to 92%, thus concurring to power saving and battery lifetime extension. Additionally, Time Slicing provides Seamless Handover to devices with single antenna, because during off-time intervals the inactive receiver is enabled to measure

Figure 2. Time slicing burst parameters the received

signal strength (RSSI) from neighboring cells to execute the handover toward the cell showing the strongest signal, without service interruption. Obviously, more measurements are taken during off time, more battery energy is wasted.

3. DVB-H Handover Related Considerations DVB-H network, like radio-mobile cellular systems, is characterized by a cellular coverage structure, which implies that handover procedures are necessary to avoid service interruptions. Handover in DVB-H is defined as a change of Transport Stream and frequency when the receiver moves from one DVB-H cell to another one while continuing its reception of IP streams. The handover mechanism shows different features depending on whether it occurs in Single Frequency Networks (SFN) [12] or in Multi Frequency Networks. In Single Frequency Networks (SFN) all transmitters use the same frequency and transmit the same TS in a synchronized manner. In Multi Frequency Networks (MFN) each transmitter uses a different frequency. According to this definition, DVB-H handover can occur within MFN networks, between two different SFN areas that are part of the same network and/or between two different networks. As shown in figure 3 different typology of handover are foreseen in DVB-H networks: handovers between cells belonging to the same subnet and the same original network (see case 1 and 3 in the figure); handovers between cells belonging to different subnets, but with the common origin network (case 2 and 4); and handovers with change of the original networks (case 5). Furthermore, the handover may involve also a change in TS (case 1, 3, and 5, when considering the dashed areas in figure 3 ). DVB-H standard, differently form mobile telephone networks, does not require a return channel, so that the whole handoff process (from its beginning to its completion) is managed by the receiver (passive handoff). In this case, the seamless handoff is made possible by means of the above cited time-slicing technique. Nevertheless, it would be possible to perform an active handoff whenever terminals are equipped with both DVB-H and cellular communication capabilities. In this case, the dualmode terminal can rely on an interactive channel, such as a cellular return channel [ 13-14] to be used during handoff. ,

Figure 3. Handovers Typologies

The scientific community agrees in outlining the DVB-H passive handover procedures in three different phases [11]: (i) Handover Measurement; (ii) Handover Decision; (iii) Handover Execution. During Handover Measurement, the DVB-H terminal monitors the signal strength fluctuation from the serving cell until the received signal is above a given threshold. Whenever the signal strength decreases, then the terminal has to turn-on the receiver during the Off-Time to receive signal strength measurements also from neighboring cells. Subsequently, the Handover Decision is triggered and obtained signal are compared with each other and with the current signal strength, to the purpose of evaluating if a better transmitters exists with respect to the current serving one. Finally, during the Handover Execution, the signals of the targeted handover cell (chosen during the handover decision phase) are synchronized, and the transmission can, subsequently, continue without interruption. Two key problems exist in DVB-H systems that make the handover procedures described above inefficient, and, somewhat, ineffective in terms of terminal power consumption. These two critical features can be summarized as follows: •

Ping Pong effect: Because of shadowing and multipath-fading effects, the signal strength received by the DVB-H terminal can quickly fluctuate while the user roams within a serving cell. In such a situation, it could happen that the receiver detects a stronger signal from a neighboring cell, even when it is still far from the current cell borders. In this case, an unnecessary handoff is likely executed. In fact, the receiver will perform a further handover back to the old cell as soon as the signal from this cell become again stronger. This behavior, called Ping Pong effect, causes a significant terminal power consumption. A reduction in the Ping Pong effect is an open issue in DYB-H handoff management, as it will be shown in the next section.

• Fake signal occurrence: The Handover Decision algorithm has to evaluate if signals received from the neighboring cells are “possible” or “fake” signals. A “possible signal” is a signal that has been found in the NIT of the current network and which carries the requested services [11]. While, a “fake signal” is a signal that has a similar frequency to any one of the frequencies found in the NIT, but it is provided from another network [11]. The fake signal occurrence can cause service interruption and, like the ping-pong effect, terminal power degradation. Also the reduction of fake signal occurrence is an open issue. Handover algorithms in DVB-H systems are quite a novel issue and, in the literature, many solutions to manage user mobility are proposed. In the next section, a brief overview of recent approach to improve the system performance during the handoff procedure is

given.

4. DVB-H Handover Proposals The first DVB-H handoff algorithm presented in literature by Puputti in [ 11 ] bases its Handover Measurement phase on the Received Signal Strength Indication (RSSI) parameter. Initially, RSSI measurements are taken during the On-Time only in the serving cell. Whenever the RSSI level falls below a given threshold, then measurements are taken both in the serving and in the adjacent cells during the Off-Time. The cell with the strongest RSSI level (following the assessment that the received signal is not a fake signal) is selected as a new current cell. Moreover, in [ 11 ] it has been demonstrated that the elapsed time between two consecutive bursts (off-time) is long enough to allow the reception of several RSSI from adjacent cells and to discard fake signals. Unfortunately, RSSI values do not always provide true information about the best cell to choose, this causing Ping Pong effect and resulting battery

consumption. Hamara in [15] presented an exhaustive analysis on handoff procedures in DVB-H systems. He also proposed advanced modifications of Handover Decision procedures (with respect to [11]), by taking into account joint RSSI and BER (Bit Error Rate) value measurements. Yang et al. in [16] proposed a further method based on post-processing of measured SNR (Signal Noise Ratio) values to avoid the ping-pong effect and to discard received fake signals. The SNR is directly calculated from the RSSI measurements. The SNR post-processing, obtained by means of the CDFs (Cumulative Distribution Functions) of all the SNR values, allows a finer estimation of received signals (compared to RSSI values). Vare, Hamara and Kallio in [17] introduced an improvement in handoff performance in terms of power saving through the signalling of cell coverage areas by means of a new table (called Cell Description Table, “CDT”), which shall be added to pre-existing PSI/SI tables. By using position information, the terminal power

receiver can improve the handover decision procedure, reducing fake signal and ping pong effect. Yang et al. in [ 18] suggested the introduction of new decisional parameters into the Handover Decision procedure; this aiming at predicting the exact time instant when to trigger the handover with a consequent reduction of the handover measurement frequency. Some of the novel decisional parameters are: (i) Context Aware Handover Decision-making; (ii) Location Aided Handover Decision-making; (iii) UMTS Aided Handover Decision-making; (iv) Repeater Aided Handover Decision-making; (ν) Hidden Markov Model Based Decision-making. Schwoerer and Vesma in [19] proposed a new synchronization technique, called correlation-based “Fast Scattered Pilot Synchronization”, for DVB-H receivers to minimize the synchronization time during the Handover Execution stage. This innovative technique contributes to further reduce the terminal receiver power consumption. May in [20] starting from the consideration that adjacent cells can transmit the same Transport Stream in a not-synchronized way (by introducing different delay and jitter), proposes a new policy called “phase shifting” that allow to synchronize signals originated from neighboring cells during the Handover Execution. The “phase shifting” technique ensure the avoidance of any packet loss. In [21] a novel handover algorithm has been proposed with the aim of reducing the frequency of handoff measurements, with a consequent reduction of handled terminals power consumption with respect to the RSSI based procedure presented in [11]. The objective is accomplished by replacing RSSI measurements with MER (Modulation Error Rate) measurements as long as possible, and by activating the RSSI Handoff Measurement procedure only when the measured MER value falls below a given threshold. This means that the terminal monitors the quality of the transmission and, according to its level, decides whether it is necessary to start the RSSI measurement procedure or not. The Modulation Error Ratio (MER) of the received signal is widely accepted as a quality indicator parameter in DVB systems. It is a figure of merit used to analyze the impact of RF disturbances on the demodulation process. The main reason to choose MER as a basis for qualitybased handoff algorithms is that it is always able to give correct indication about the perceived quality of the digital vision and the consequent customer satisfaction/dissatisfaction, differently from RSSI. In fact, it may happen that a good level of perceived QoS may correspond to a low RSSI level, (this situation likely causing Ping-Pong Effect); while for a high RSSI level, a corresponding low level of QoS may be perceived (this situation could cause a Call Dropping). By summarizing, the MER exploitation allows to reduce power consumption, because the activation of the handoff procedure occurs only when the customer is actually in an overlapping area (this avoiding the ping-pong effect) and the MER measurements are carried out during the On-Time (this avoiding any power consumption during inactive periods). A further feature consist in the introduction of a MER linear prediction technique (implemented into the terminal), so that the future MER value depends not only on the current measured MER but also on the MER history. This procedure concurs to greatly improving the performance.

In [22 ] an extend version of [21 ] has been

proposed, which considers that addiin terms of are attainable by using an Active Handadvantages power saving an UMTS return channel as an interaction channel. The off procedure assuming mechanism is based on the use of terminals equipped with both DVB-H and UMTS access capability. This allows to implement a very efficient procedure, which consists in measuring the MER index during the On-Time and in performing the MER prediction within the UMTS network. Herein, in fact, it is possible to use a more tional

performing estimation

module without battery consumption limitation typical of the mobile user terminals. Therefore, a procedure of Active Handoff that transfers the prediction functionality from the dual mode terminal to the UMTS network equipments and utilizes the UMTS return channel as an interaction channel is a further performing approach to the problem.

Those cited are just a few sample proposals; a comprehensive and enlightening survey with more details about the cited handoff techniques and many others, is available in [13], and in [23].

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“

”

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Proceedings of 8th International OFDM Workshop Hamburg, Germany September 2003 [20] G. May Loss-free Handover for IP Datacast over DVB-H Networks ", IEEE ISCE 2005 ,

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Labate G. Araniti A. Molinaro A. Iera B. Orlandi ,

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DVB-H systems ", Proceeding IEEE PIMRC 2007 Athens September 2007 G. Araniti F. Calarco A. Iera A. Molinaro and B. Orlandi Active handoff in DVB-H systems with UMTS return channels ", Proceeding WPMC 2007 Jaipur, India December 2007 ,

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Tom Owens

Channel Modelling, MIMO and OFMD George T. Karetsosa a Center for Technological Research of Thessaly, Larissa, Greece Abstract. The second section of this book encompasses chapters dealing with physical layer aspects related to the 4th generation in wireless communications. In particular the scope of this section is to provide the state of the art on technologies and mechanisms that enhance the data transfer capabilities of the wireless medium and strive to make it capable to support bandwidth demanding applications at real time. In order to provide a coherent overview of the challenges and achievements in this area we have organised the chapters of his section in two clusters. The first cluster is presenting techniques and technologies for channel modelling and estimation while the second one is focusing on issues related to MIMO systems.

Section Overview Research and development related physical layer techniques is crucial for supporting the envisaged applications for 4G wireless communications and systems. This section of the volume presents a collection of chapters that highlight the progress in certain key technological areas related to physical layer enhancements. As we already mentioned the first set of chapters is devoted on channel modelling and estimation. The first chapter of this cluster is dealing with “Adaptive OFDMA Systems” and is co-authored by Dania Marabissi, Daniele Tarchi and Romano Fantacci. The authors introduce the basic principles of adaptive OFDMA by focusing on those most important parameters that can be adjusted in order to achieve better performance. Amongst several adaptation rules, they focus on the adaptive modulation and coding and adaptive subcarrier allocation that offer higher flexibility. Overall the chapter has an overview nature and each adaptation type is introduced also by considering some examples of algorithms and by showing their performance results in typical communication scenarios.

Heidi Steendam and Marc Moeneclaey are the authors of the second chapter on channel estimation and modelling that presents “Bounds and Algorithms for Data-Aided Channel Estimation in OFDM”. The authors consider three types of guard intervals: cyclic prefix (CP), zero padding (ZP) and known symbol padding (KSP). Based on the ML principle, (sub) optimal channel estimators are derived, and the MSE of the estimators is compared to the corresponding Cramer-Rao bound. The authors show that CP-OFDM channel estimation outperforms the other techniques. However, the performance of the other channel estimators is close to the performance of the CP-OFDM channel estimator. Furthermore the authors highlight that the performance of the estimators is essentially independent of the FFT size. Chapter three by Ryosuke Uchida is dealing with the subject of “Distributed Space-Time Block Coding for Large Set of Relay Terminals”. The author presents a

DOI: 10.1201/9781003336853-13

Channel Modelling, MIMO and OFMD decode-and-forward cooperative diversity scheme for a wireless packet transmission network with large and undetermined set of relay terminals. In such a situation, diversity order of the random selection cooperative relaying schemes is shown to be decreased due to duplicated mapping of the same column vector of the STBC matrix to multiple RTs. This chapter discusses a signaling scheme to reduce the performance loss by introducing the linear transformation of the STBC matrix by a signature vector, which has more degrees of freedom for the assignment of signals compared to the conventional STBC-based cooperative diversity.

In the fourth chapter Dieter Van Welden Frederik Simoens, Heidi Steendam and Marc Moeneclaey present “A Comparison Between Parametric and Nonparametric Channel Estimation for Multipath Fading Channels” in terms of the MSE on the received symbol pulse. The MSE consists of two terms, caused by the modeling error and the estimation error, respectively. For both methods the authors derive the respective Cramer-Rao lower bound on the part of the MSE caused by the estimation error. The influence of the number of estimated paths for the parametric estimation method and the number of estimated channel taps for the nonparametric estimation method is investigated. It is shown that for every Es/N0 the number of parameters to be estimated can be optimized so that the MSE is minimized and that the nonparametric estimation method is outperformed by the parametric estimation method in terms of the MSE on the received symbol pulse. The fifth chapter by Zhuwei Wang and Xin Zhang is entitled “Envelope Correlation Analysis of MRC Signals in Correlated Rician Fading”. The authors analyze the envelope correlation coefficient (ECC) of the maximal ratio combining (MRC) output over correlated Rician fading channels and then compare the characters of ECC in different environments considering the noise and channel estimation error. They also present the system’s performance based on average capacity and outage probability. Finally, they provide the relation between the ECC and system performance in the stationary environment which becomes simpler because ECC can replace the impacts of Rician factor and channel attenuation of each path. An “Experimental Investigation of Channel Estimation for IEEE802.11b WLAN System” by Yu Imaoka, Hiroshi Obata, Yohei Suzuki, and Yukitoshi Sanada is provided in chapter six. In the IEEE802.11b WLAN standard, directsequence / spread-spectrum (DS/SS) modulation is employed. With a fractional sampling RAKE receiver, it is possible to achieve diversity and reduce the BER in DS/SS communication. In order to realize the diversity through fractional sampling, an impulse response of the channel must be estimated. For that the authors rely on a pseudo-inverse matrix with a threshold. It is concluded that the channel can be estimated precisely with the optimum threshold and that the accuracy of channel estimation in the case of the LOS situation is better than that of the NLOS situation. Concluding the set of chapters that are focusing on channel modeling and estimation Dheeraj Sreedhar is presenting “Hybrid -ARQ Techniques and its Application in 4G Wireless Systems”. This chapter covers in detail the study and analysis of the recent developments in H-ARQ as well as MIMO H-ARQ and provides

Section Overview

a link with the second cluster of chapters of this section that deals with MIMO systems. H-ARQ is a modification of conventional ARQ techniques implemented by the link/transport layer, wherein the receiver requests for a re-transmission of an in-correctly received packet or alternatively, the transmitter keeps transmitting a packet until an acknowledgement for it is received. With H-ARQ when a receiver feedback for a transmitted packet is available at the transmitter, for a given spatial multiplexing gain of a MIMO channel, the reliability of the channel, measured in terms of maximum achievable diversity, is enhanced. Finally deployment and application of H-ARQ and MIMO H-ARQ in IEEE 802.16e is covered. The second cluster of chapters is focusing on MIMO systems which are becoman ing integral part of today’s and particularly of future communication systems. In the first chapter of the cluster related to MIMO systems Xing Zhang and Wenbo Wang provide “Theory and Performance of Multiuser Diversity in MIMO Systems”. In particular they present a comprehensive framework to analyze the performance of multiuser diversity (MUD) in multiple-input multiple-output (MIMO) systems. Based on this framework, the tight closed-form expressions of outage probability, outage capacity and average symbol error rate of multiuser diversity are derived for the MIMO transmit antenna selection with maximal-ratio combining (TAS/MRC) system. From that, it is shown how antenna selection gains, MIMO antenna configurations and fading gains impact on the system performance, with an emphasis on the study of multiuser diversity ( MUD) influence. From both theoretical and simulation results, the study shows that in MIMO TAS/MRC systems the number of users plays a key role in the system performance and can be viewed as equivalent “virtual” transmit antennas, which is the source of the inherent multiuser diversity gain. H. Farhat, R. Cosquer and G. El Zei provide an overview on “MIMO Channel Characterization for Future Wireless Communication Systems”. In particular it highlights different aspects concerning the MIMO propagation channel starting with a brief overview regarding its modeling and characterization. The authors show that, in the MIMO context, the knowledge of the spatio-temporal channel response appears essential for future wireless systems simulation and in order to obtain more realistic MIMO channel models, extensive measurement campaigns are needed, considering different environments and frequency bands The third chapter by Christian A. Hofmann and Andreas Knopp covers the subject of “Optimal Indoor MIMO Line-Of-Sight Wireless Channels” The authors show that with optimized antenna arrangements even the maximum multiplexing gain can be achieved in LOS channels which are generally considered as less appropriate for MIMO applications. It is proven that the NLOS signal parts are not harmful to the capacity of LOS optimized channels and even beneficial for channels with a suboptimal antenna setup. Channel measurement results at 2.4 GHz are taken into account showing promising results for the channel capacity in indoor LOS environments. In the fourth chapter Yuanyuan Fei and John Thompson deal with the “Design of Compact Antenna Arrays for MIMO Wireless Communications”. The authors discuss how mutual coupling can be properly modeled in a MIMO wireless system.

They also discuss how simple matching networks that take into account the mutual coupling effect can be used to provide significant performance improvements in compact antenna array receivers. They provide simulation results for a 2×2 MIMO system to verify the effect of different matching networks and show results for the sensitivity of MIMO performance to errors in the matching network components and antenna element dimensions. The presented results show that optimizing a single-port matching impedance is a simple but promising approach to improve the performance of compact arrays. Massinissa Lalam, Karine Amis and Dominique Leroux in the fisth chapter present “Space-Time Error Correcting Codes and Iterative Decoding'’ for MIMO systems. The space-time error correcting codes (STECCs) are an efficient new spacetime block code family built from any linear forward error correcting code (FEC) for two transmitters. The authors show that the use of a turbo equalisation principle significantly reduces the detection complexity, which becomes linear with the number of modulation symbols to recover. The sixth chapter of this section is written by Nizar Zorba and Ana I. PéerezNeira and deals with the “Performance Evaluation of MIMO Multiuser Opportunistic Schemes under QoS Requirements”, The authors present a transmission strategy where a minimum rate per user is required, within a given time interval to satisfy maximum delay restrictions. Both demands stand as the Quality of Service (QoS) indicators for the system behaviour, and they are both presented in closed form expressions. The authors show that in order to simultaneously fulfil these requirements, a trade-off on the number of available users should be obtained. A Cross-Layer Call Admission Control (CAC) is then proposed to regulate the number of users, where the CAC objective is to keep the multiuser gain of the opportunistic system, while satisfying the users" QoS requirements in terms of minimum rate and maximum scheduling delay. In summary this section provides a comprehensive overview of certain key developments in the areas of channel modeling and estimation as well as in MIMO systems. We have tried to keep a balance between articles that are of tutorial nature and articles that present novel technological enhancements required for the success of the 4th generation of mobile and wireless communications.

Adaptive OFDMA Systems* Dania Marabissi, Daniele Tarchi, Romano Fantacci Università degli studi di Firenze, Italy e-mail: {marabissi,tarchi,fantacci}@lart.det.unifi.it Abstract. Modem wireless communications are based on the exploitation of channel behavior

and/or user requirements by adapting one or more transmission parameters. Amongst several systems the OFDM A offers a lot of capabilities to the system designer allowing adapting in several ways the communications. This chapter deals with the introduction of the basic principle of an adaptive OFDMA system by focusing on those most important paramethat can be adjusted in order to have better performance. Finally, presented also by showing some numerical results. ters

some

techniques

are

1. Introduction Multimedia high speed wireless communication systems usually suffer of a severe performance degradation due to frequency selective fading effects. Orthogonal frequency division multiplexing (OFDM) technology has the capability of mitigating frequency-dependent distortion across the channel band and simplifying the equalization in a multipath fading environment. The basic principle of OFDM is parallelization: by dividing the available bandwidth into several smaller bands that are called subchannels, the transmitted signal over each subchannel may experience flat fading. The properties associated with OFDM have led to its consideration as a candidate for high rate extensions to third-generation communication systems as well as for fourth-generation mobile communication systems [1],[2]. To have more flexible and higher efficient OFDM systems, the adaptive OFDM schemes are adopted to maximize the system capacity and maintain the desired system performance [3 ],[ 4 ], In particular, in an OFDM wireless system, the inherent multi-carrier nature of OFDM allows the use of link adaptation according to the behavior of the narrow-band channels: the bit-error probability of different OFDM subchannels, transmitted in time-dispersive channels, depends on the frequencydomain channel transfer function [3 ],[ 4 ]. Transmission techniques which do not adapt the transmission parameters to the fading channel require a fixed link margin or coding to maintain acceptable performance in deep fades. Thus, these systems are effectively designed for the worst-case channel conditions, resulting in insufficient utilization of the full channel capacity. Conversely, if the channel fade level is known at the transmitter, Shannon capacity is achieved by matching transmission parameters to time-varying channel: the signal

* This work has been supported by MIUR under project FIRB “Insyeme”.

DOI: 10.1201/9781003336853-14

Adaptive OFDMA Systems

transmitted to and by a particular station can be modified to account for the signal quality variation. Traditionally, wireless systems use power control as the preferred method for link adaptation. In a system with power control, the power of the transmitted signal is adjusted in order to maintain the quality of the received signal at each individual subchannel. Therefore, the transmit power will typically be low when a user is close to the BS and it will increase with the distance from the BS. Power control is based on the water filling theorem: given a certain power budget, more transmit power is applied to frequencies experiencing lower attenuation. Thus, given the transfer function, the optimal power distribution is similar to inverting the transfer function and pouring a liquid (i.e., power) into the shape [5]. Although the use of power control on its own can improve the system performance in terms of the bit error rate (BER), the total channel capacity is not used efficiently at any transmission time, due to the fixed modulation used. To address this issue, adaptive modulation and coding (AMC) or subcarrier allocation should be considered. In a system with AMC, the power of the transmitted signal is held constant but the modulation and coding orders are changed to match the current received signal quality. Users close to the BS are typically assigned higher-order modulations and higher code-rates but the modulation-order and/or the code-rate will decrease as the distance from the BS increases [6],[7]. Furthermore, in a multiuser OFDM wireless network, the given system resources are shared by several terminals and, in particular, in an OFDMA (Orthogonal Frequency Division Multiple Access) system disjunctive sets of subcarriers are allocated to different users, to provide a flexible multiuser access scheme [7 ]. The channel characteristics for different users are almost mutually independent in multiuser environments; the more attenuated subcarriers for a user may result not to be in a deep fade for other users, therefore an OFDMA wireless network may benefit from multi-user diversity dynamically assigning subcarriers with the best frequency response to the users.

All the cited transmission parameter adaptation schemes need channel state information (CSI) estimates to efficiently react to the changes in channel quality. Clearly, this estimation of future channel parameters can only be obtained by prediction from past channel quality estimations, hence, the adaptive system can only operate efficiently in an environment exhibiting relatively slowly varying channel conditions. The accuracy of the channel estimates and the delay between the channel quality estimation and the actual transmission of the OFDM symbol in relation to the maximal Doppler frequency of the channel is crucial to the adaptive system’s performance [6]. If the communication between the two stations is bidirectional and the channel can be considered reciprocal, then each station can estimate the channel quality on the basis of the received OFDM symbols and adapt the parameters of the local transmitter to this estimation without feedback (open-loop adaptation). If the channel is not reciprocal, as in a frequency-division duplex (FDD) system, then the stations cannot determine the parameters for the next OFDM symbol's

2. Adaptive Algorithms

transmission from the received symbols. In this case, the receiver has to estimate the channel quality and explicitly feedback this perceived channel quality information to the transmitter in the reverse link (closed-loop adaptation). A method to eliminate feedback is pre-equalization. Based on the estimated frequency-domain channel transfer function, spectral pre-equalization at the transmitter can be invoked, in order to partially or fully counteract the frequency-selective fading. Unlike frequency-domain equalization at the receiver, which corrects for the amplitude and phase errors inflicted upon the subcarriers by the channel, spectral pre-equalization at the OFDM transmitter can deliver near-constant signal-to-noise levels for all subcarriers. Flence the above concept can be interpreted as power control on a subcarrier-by-subcarrier basis. The design of link adaptation strategies can benefit of a cross-layer optimization approach (i.e., the joint de sign of the MAC and PHY layers), that attempts to dynamically match the requirements of data link connections to the instantaneous available physical layer resources and to the CSI [4 ],[ 10]. The transmission parameters are selected at the physical layer to match the wireless channel, but they must take into account also the information coming from the higher levels, in particular from the MAC layer. For example, existing AMC schemes are mainly based only on the CSI available at the physical layer and rely on the assumption that data are continuously available at the transmitter: modulation-coding schemes are chosen at the physical layer to match the wireless channel, there are sufficient data waiting to be transmitted in the queues (buffers) at the data link layer. However, in practical communication systems with randomly arriving data streams, the queues may be empty from time to time, even though the wireless channel can accommodate transmissions. On the other hand, the service process of the queue feeding is affected by the wireless medium, and depends on how the AMC module adapts its parameters to channel variations. The interaction of queuing at the data link layer with AMC at the physical layer provides interesting design problems. In addition QoS (Quality of Service) requirements imposed by the MAC layer can impact the modulation and coding scheme to be selected [10].

2. Adaptive Algorithms Main aims of link adaptation algorithms are to maximize the overall network throughput, to achieve target error performance, or to minimize the overall transmit power.

By using throughput maximization, the transmitter can send data with higher transmission rates over the subcarriers with better conditions so as to improve throughput and simultaneously to ensure an acceptable bit-error rate (BER) on each subcarrier. It is sometimes unfair to those users far away from a base-station or with bad channel conditions. On the other hand, absolute fairness may lead to low bandwidth efficiency. Therefore, an effective tradeoff between efficiency and fairness is desired in wireless resource allocation.

The alternatives can be to determine the optimal power allocation in order to minimize the transmit power subject to a rate constraint or to fix a target error rate to be satisfied. The research of an optimal solution for an efficient resource assignment (power, subcarrier and AMC scheme) is a difficult task and a lot of research work is currently on going on developing sub-optimal solutions at low cost. In this section examples of adaptive OFDMA techniques are presented. 2.1. System Model The

adaptive OFDMA system presented here is based on a TDD (Time Division Duplexing) transmission that is considered the most suitable solution for data traffic such as new IP based multi-rate and multi-QoS services. A balanced division of the frame, dividing it into 40 OFDM symbols for the Downlink (DL) subframe and 39 OFDM symbols for the Uplink subframe has been chosen. The system has K users that communicate with the base station, and Ni carriers assigned to the i-th user, under the form of slots: the slots are composed by 18 subcarriers contiguous in frequency over 3 contiguous OFDM symbols.

are

The operation of link adaptation is performed in the downlink on a frame basis. Since the fraction of the spectrum which is employed for the uplink and the downlink is the same, we can assume the channel as reciprocal in the frequency domain. Thus, after estimating the channel response in the uplink of the current TDD frame, its behavior can be used in the following DL frame. The estimation of the channel coefficients is performed by the BS in the Uplink subframe. It is important to underline that even if a perfect knowledge of the channel impulse response at the receiver is assumed, the time delay introduced by the channel estimation algorithm is taken into account. The link adaptation is done considering the channel state at the previous frame and, therefore, the aforementioned delay can introduce a performance loss in time varying channels. A Rayleigh multipath channel (ITU-Vehicular A, [18]) with a terminal maximum speed of 125Km/h has been considered, with a frequency of 3.5GHz and a bandwidth of 10MHz. The Fast Fourier Transform used to generate the OFDM symbols has 1024 points. 2.2. Adaptive Modulation and Coding Adaptive modulation and coding (AMC) appropriate modulation and Coding

allows OFDMA systems to select the scheme depending on the propagation conditions of the communication channel, e.g., during good propagation conditions a high order modulation scheme with low coding redundancy is used in order to increase the data rate of the transmission, while during a signal fade, the system selects a modulation scheme and a coding rate of lower order to maintain both connection quality and link stability without the need of increasing the signal power.

most

In [12],[13] two adaptive modulation and coding methods for an OFDMA system are proposed. The aim is to develop some techniques that maximize the

Figure 1. Moore’s state machine for raising modulation and coding rate

system performance in terms of some QoS metric, with a particular attention to error probability and throughput. The first proposed technique, called Target BLER (Block Error Rate) aims to respect a maximum preset target BLER imposed on the basis of a target QoS level. The second technique is designed in order to maximize the throughput parameter without any explicit constraint on error rate. Both techniques use the same system structure; the AMC system is modeled as a Moore’s state machine, shown in Figure 1 where each state is represented by a couple formed by a modulation order and a coding rate: the envisaged modulations are QPSK, 16-QAM and 64-QAM with the coding rate 1/2 and 3/4. The aim of this model is to create a universal machine that can be adapted easily to different AMC techniques following the user requests and/or the system characteristics, with the possibility of integrating higher modulation orders and different coding rates or coding methodologies. Each adaptation algorithm is basically characterized by five thresholds (A, B, C, D, E) representing the changing events between different transmission schemes: the averaged channel attenuation factor over a slot is compared with the thresholds, when a threshold is reached, the modulation order and/or the coding rate change and the state machine keeps a different state until another threshold is reached. The QPSK modulation with coding rate 1/2 state is always used at the beginning of the communication, supposing that the BS has no further ,

information about the channel conditions. The thresholds are calculated by means of theoretical analysis. The main difference between the two adaptation algorithms and their behavior is how thresholds are calculated.

Target Block Error Rate Technique The Target BLER technique has been introduced as a method for keeping the error rate under a target limit, maintaining a fixed level of quality of service in terms of error probability: even if this method is fundamentally conservative, it allows to enhance performances compared to non-adaptive strategies by selecting

Figure 2. Calculation of thresholds for state change: (a) for a target BLER; (b) for the maximum throughput

the most efficient transmission scheme which guarantees the respect of the error rate constraint. In this work a block coder with dmin = 3 and Maximum Likelihood decoding algorithm have been considered. To determine the thresholds, the expression of a block error probability (Pblock) in a Rayleigh multipath fading has been derived by means theoretical analysis [14]. The Target BLER technique has one degree of freedom, represented by the imposed target BLER; different values of the target correspond to different system performances. For each value of SNR we can find the BLER value as a function of the channel attenuation factor, and establish five target attenuation factor values in correspondence of which the switch of modulation and coding scheme is performed. The switching values are those that assure the target BLER, for a certain SNR and a certain scheme. The thresholds can be found by selecting the channel attenuation corresponding to which the Pblock is equal to the Target BLER, BLER target. In Figure 2 (a) it is shown how the thresholds for state i.e., Pblock changing procedure are defined; in particular the thresholds calculation for a SNR 16 dB and a target BLER equal to 8.10-3 is depicted. The figure shows the behavior in terms of block error probability for different attenuation factor values. =

=

Maximum Throughput Technique The Maximum Throughput algorithm reflects an opposite approach with respect of the previous technique and aims to maximize the total link throughput by interpolating the throughput curves of the used modulation and coding scheme at their maximum value. Hence, the transmission efficiency is enhanced but the performance in terms of error rate becomes worse, since no constraint on maximum acceptable error probability is given. Differently from the first discussed method, this adaptive technique is less conservative and more devoted to such services that request the maximum achievable data rate, with a lower sensibility to the error rate; therefore this system is best suited for video streaming or VoIP services.

From the systemic point of view this method presents no deep differences toward the target BLER technique; the thresholds calculation procedure is the only point of divergence. In particular, the attenuation factor thresholds are established as those values corresponding to which the throughput curves for different schemes have the same value, with the aim to select, for each frame and each SNR, the modulation order and the coding rate that maximize the total throughput. This technique has no degree of freedom. The throughput is expressed as the average useful bits per symbol for different SNR values at the transmitter side considering the slot structure of the proposed system.

The Maximum Throughput algorithm allows selecting the most efficient scheme in terms of throughput for a certain SNR value. In Figure 2(b) it is shown how the threshold for state change are defined; in particular herein it is supposed to have a SNR = 20 dB. The figure shows the behavior in terms of throughput for different values of attenuation factor. Performance Comparison Some examples of results are presented in order to better explain the previous described adaptation algorithms. In Figure 3, the performance in terms of BLER is compared between the two proposed techniques. The Target BLER technique considers three different values to be guaranteed by the adaptation algorithm, i.e., TBLER = 5 · 10−2, TBLER = 10−3 and TBLER = 5 · 10−3. In Figure 4 the performance comparison in terms of throughput is shown. The best BLER performance can be achieved by using the Target BLER (with TBLER 5 10-3). It is evident that if the Target BLER value is higher, the BLER performance worsens. The BLER curves behavior is inverted in the Throughput curves. From the throughput point of view, the best case is represented by the Maximum Throughput method that is always higher of the static modulation throughput. The Target SER technique has been designed for ensuring a generic target BLER, with the possibility of modifying that value whenever the QoS requirements of a specific application change. =

•

Figure 3. BLER comparison

Figure 4. Throughput comparison

2.3 Adaptive Subcarrier Allocation One other issue to be considered in adaptive OFDMA systems is the subcarrier allocations. In an OFDMA system, the resources can be distinguished both in frequency and in time dimension: different users can be assigned subcarriers belonging to different frequencies or to different OFDM symbol times within the frame. Thanks to the channel state information (CSI), it is possible to determine the channel capacity that a user achieves by the assignment of a certain slot. Hence, the slots can be assigned to the users so as to achieve (or to approximate) a certain channel capacity distribution among the users.

In an OFDMA frame one user does not use a subcarrier continuously, hence, the channel capacity is limited by the duration of a single OFDM symbol. The total channel capacity must be divided by the number of OFDM symbols per frame (Ns) in order to obtain the capacity belonging to a single subcarrier in a frame [14]: up er C Subscript k times comma up er O up er F up er D up er M up er A Baseline times equals times StartFraction 1 Over up er N Subscript s Baseline Subscript Baseline EndFraction up er B Subscript p Baseline log Subscript 2 Baseline times left-parenthesi 1 times times plus times times up er S up er N up er R right-parenthesi times

where Bp is the carrier bandwidth (corresponding to the total system bandwidth divided by the number of carriers), and SNR is the signal to noise ratio of the intended subcarrier. SNR takes into account also the effects of the multipath channel. Thus, considering the SNR almost constant within the carriers of a slot, the capacity of an N × M rectangular slot (N contiguous carriers in the frequency domain per M OFDM symbols) is: up er C Subscript s l o t Baseline times equals times StartFraction up er N times period times up er M Over up er N Subscript s Baseline Subscript Baseline EndFraction up er B Subscript p Baseline times log Subscript 2 Baseline times left-parenthesi 1 times plus times times up er S up er N up er R right-parenthesi

it

The goal of the allocation algorithms is a certain slot assignment to the users: be expressed through a matmatrixX, rix whose dimensions are A rows per B columns

can

(A slots along the frequency dimension and B slots along the time dimension), that holds in each position Xi,j the index of the user to whom the slot (i, j) is assigned: Xi,j = k if the slot (i, j) is assigned to the k-th user. Hence, the channel capacity assigned to the k-th user by a certain slot allocation algorithm is: up erCSubscriptkBaselinetimesequalstimesnormalup erSigmaUnderscriptiequals0Overscriptup erAminus1Endscriptstimesnormalup erSigmaUnderscriptjequals0Overscriptup erBminus1Endscriptstimesdeltatimesleft-parenthesi kminusup erXSubscriptitmescom ajBaselineright-parenthesi timesup erCSubscriptup erSlotBaseline

where: delta times times left-parenthesi x right-parenthesi times times equals times left-brace times StartLayout 1st Row 1st Column 1 2nd Column i f times x equals 0 2nd Row 1st Column 0 2nd Column i f times x not-equals 0 EndLayout

Fair allocation A fair allocation algorithm approximates a fair capacity distribution, where each user obtains the same amount of capacity [15]. Each possible slot allocation has a different set of capacity values for the users: the expected solution is that whose values of Ck are approximately equal. This can be obtained searching for the slot allocation whose minimum value among all the Ck has the highest value among all the possible allocations, in order to reduce the differences of capacity among the users. Hence, the particular allocation that maximizes the minimum value among all the Ck is searched: normal up er X times equals times arg times max Underscript x Endscripts times left-parenthesis min Underscript k Endscripts up er C Subscript k Baseline times right-parenthesis

A

suboptimal solution is searched through an iterative algorithm. The algoafter an initialization phase, assigns to each user a slot within the frequencies rithm, in which the user has the best channel conditions. Subsequently all the remaining slots are assigned through an iterative process: for each iteration, the user with the lowest amount of capacity is selected and a slot is allocated to him; the slot is selected among the ones that provide the best SNR to that user. The selection of the user with the lowest capacity is fundamental to obtain an approximately equal distribution of capacity; furthermore, the slot selection depends on the channel conditions of the user, in order to exploit the multiuser diversity. Proportional allocation In the proportional allocation the users with the best channel conditions obtain a larger amount of capacity: capacity values assigned to the users are proportional to the maximum capacity that is the amount of capacity that corresponds to the assignment of all the slots to that user [16].

The solution is an iterative algorithm where the main difference with the previous one is the user selection: in this case, the selected user is the one who has the minimum ratio between the temporary value of capacity and the value of the maximum obtainable capacity. Equal capacity increment allocation The goal of the third strategy is to provide to each user an equal increment of capacity with respect to a non-adaptive strategy [ 16]. This technique attempts to distribute the additional amount of capacity equally among all the users. In particular, the value of capacity resulting to each user through a non-adaptive technique is estimated; subsequently, the slot allocation that provides, for each user, an equal increment of capacity with respect to the estimated value is looked for. Let’s consider a notadaptive strategy in which the slots belonging to different users are distinguished only by the position in the time domain (that is a TDMA system); in this case, the different channel conditions a user has on different frequencies are averaged and, therefore, the amount of capacity assigned to the k-th user is: up er C overbar Subscript k Baseline times equals times StartFraction 1 Over up er K EndFraction up er C Subscript max times comma k Baseline

This value is used as an estimation of the capacity of a not-adaptive algorithm. Let’s define Gk the difference between the capacities assigned to the k-th user and the estimation of a non-adaptive algorithm capacity. The value Gk represents the capacity increment for the k-th user with respect to a non-adaptive strategy: the allocation in which Gk is approximately equal for all the users is searched. Similarly to the fair allocation solution, this goal is obtained by maximizing the minimum value of Gk among all the users; as a consequence of this, the solution is: normal up er X times times equals times arg times max Underscript x Endscripts left-parenthesis min Underscript k Endscripts times up er G Subscript k Baseline right-parenthesis

The main difference between this algorithm and the fair allocation consists in the user selection: the user, for which the value of Gk is the minimum, is selected, so as to make approximately equal the capacity increment C for all the users. Performance Comparison Results have been obtained through computer simulations. The used modulation schemes are QPSK, 16QAM and 64QAM. As explained before the proposed adaptive algorithms are based on the estimation of the channel capacity of the slots, in the simulations, an upper limitation to this estimation, depending on the used modulation scheme, was considered, in order to avoid an overvaluation of the slot capacity. The upper limitation is given by: up er R Subscript max Baseline times equals times StartFraction up er N period times times up er M n Over up er N Subscript Baseline Subscript s Baseline EndFraction up er B Subscript p Baseline

Figure 5. Throughput performance in absence of pathloss

where n is the number of bits per symbols corresponding to the used modulation scheme. The numerical results are shown in terms of throughput of the reference user; the previously described maximum throughput adaptive modulation technique has been used. Firstly, the systems have been studied without considering the effect of pathloss; this case corresponds to a particular user distribution where each one is at the same distance from the base station and the differences in SNR among different caused only by the effect of multipath fading.

users are

Figure 5 shows an increase of performance by using adaptive strategies with respect to a fixed allocation scheme, but the absence of pathloss makes the channel condition of all the users similar: as a consequence of this, the behavior of the three adaptive schemes is also similar. Subsequently, the effect of pathloss has been considered. The pathloss model is based on [17]. Due to the presence of pathloss, the average SNR of different users (i.e., different distances from the base station are considered) is different. A cell radius of 10 km has been chosen and the system must provide an average SNR of 7 dB at the edge of the cell. The number of users is set to 20 and their positions are randomly distributed within the cell; the performance of a single user has been evaluated with respect to the distance from the base station: the simulations have been repeated with different positions of the reference user. In Figure 6 The comparison of the three adaptive strategies with a fixed (nonadaptive) slot allocation shows an increase of performances for the proportional and the equal increment allocation with respect to the fixed one: the user obtains more channel capacity (and thus more throughput) at any distance from the base station. In particular, the proportional allocation has the best performance for distances up to 7 km and, anyway, it is better than a fixed allocation even for higher distances. The fair allocation shows an almost constant throughput for any distance, resulting

Figure 6. Throughput performance in presence of pathloss

disadvantageous for the users near the BS (because it has a lower throughput than a fixed allocation) and profitable for the users far from the BS.

3. Conclusions OFDMA technique makes easier the adaption in wireless communications allowing achieving better performance results. Amongst several adaptation rules, the attention has been focused on the adaptive modulation and coding and adaptive subcarrier allocation that offer a higher flexibility to the communications. In particular each adaptation type has been introduced also by considering some examples of algorithms and showing their performance results in typical communication scenarios.

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Bounds and Algorithms for Data-Aided Channel Estimation in OFDM Heidi Steendam and Marc Moeneclaey TELIN Department, Ghent University, Belgium Abstract. In this paper, we consider data-aided channel estimation for OFDM systems. We consider three types of guard intervals: cyclic prefix (CP),zero padding (ZP) and known symbol padding (KSP). Based on the ML principle, (sub)optimal channel estimators are derived, and the MSE of the estimators is compared to the corresponding Cramer-Rao bound. For CP-OFDM and ZP-OFDM, the channel estimator is optimal and the MSE reaches the corresponding Cramer-Rao bounds. The channel estimator for CP-OFDM slightly Outperforms the one for ZP-OFDM. Optimal channel estimation for KSP-OFDM turns out to be very complex, and the true Cramer-Rao bound is difficult to obtain. Therefore, we consider a number of sub-optimal channel estimators for KSP-OFDM and compare their MSE with the Gaussian Cramer-Rao bound. The frequency-domain estimator for KSP-OFDM has a MSE performance that is only slightly worse than the MSE performance of the optimal

estimators for CP-OFDM and ZP-OFDM.

Keywords: OFDM systems, guard interval techniques, data aided channel estimation, Cramer-Rao bound.

1. Introduction Because of its ability to achieve a high capacity per unit bandwidth and its robustchannel dispersion, the multicarrier (MC) technique is being considered for application in future mobile and wireless communication systems [ 1 ], To cope with channel dispersion, a guard interval with a length larger than the channel impulse response is inserted between blocks of data. In the literature, different types of guard intervals are discussed. The most commonly used guard interval type is the cyclic prefix (CP) [2 ]—[ 3 ]. In CP-OFDM, the guard interval consists of a cyclic extension of the transmitted MC block: the last v samples of each block of N samples are copied and added as a prefix to the MC block, as shown in Figure 1(a) At the receiver, the samples in the guard interval are neglected, and only the N samples outside the CP are kept for further processing (see Figure 1(b) ), As, the signal during the guard interval contains no new information, the CP technique suffers from a power efficiency loss with a factor N/(N + v). To avoid this power efficiency loss, the zero padding (ZP) technique can be used [2 ]—[3 ], where the guard interval is inserted as a postfix to each MC block. In this technique, no signal is transmitted during the guard interval. At the receiver, the v samples from the guard interval are added to the first samples v of the MC block (as shown in Figure 1(b) ) to maintain the orthogonality between the carriers; the resulting N samples outside the guard ness to

.

DOI: 10.1201/9781003336853-15

Bounds and Algorithms for Data-Aided Channel Estimation in OFDM

Figure 1. a) Transmitted and b) received signal for CP-OFDM, ZP-OFDM and KSP-OFDM

interval

are used for further processing. In the ZP-OFDM technique however, the noise power is increased with a factor (N + v)/N as compared to CP-OFDM as in ZP-OFDM the noise from the guard interval is added to the first v samples to be processed. Another, recently proposed guard interval technique is the known symbol padding (KSP) technique [4 ]—[ 7 ]. In this guard interval technique, the guard interval contains v known samples and is added as a postfix to each MC block; this corresponds to the dark grey area in Figure 1(a) At the receiver, first the signal corresponding to the known samples is subtracted from the received signal, and then, similarly as in ZP-OFDM, the samples from the guard interval are added to the first v samples from the MC block; the resulting N samples from the data part are then further processed. Although the KSP-OFDM technique suffers from both power efficiency reduction (as in CP-OFDM) and noise power increase (as in ZP.

OFDM), these effects however will be small when

N

v. On the other hand, the

> >

samples from the guard interval in KSP-OFDM result in an improved timing synchronization ability than in CP-OFDM and ZP-OFDM, as the low complexity timing synchronizers as in Schmidl and Cox [8 ] suffer from an ambiguity of the timing estimate equal to the length of the guard interval, whereas in KSP-OFDM, this ambiguity problem can be avoided by properly selecting the guard interval samples. As data detection algorithms require the knowledge of the channel, reliable channel estimation is necessary for the abovementioned OFDM systems. Most common channel estimation algorithms are data aided, i.e. in the OFDM signal, pilot symbols are inserted to enable reliable detection of the channel. In this paper, we will consider maximum-likelihood (ML) based data-aided channel estimation techniques for the different abovementioned OFDM systems, and compare the mean squared error (MSE) of the proposed channel estimation techniques. Further, the MSE of the estimators is compared with the corresponding Cramer-Rao bounds (CRB). known

2. Data-Aided Channel Estimation

2. Data-Aided Channel Estimation 2.1. ML Estimation and the Cramer-Rao Bound In the

that the channel changes slowly as compared to the symbol and define the vector of L channel taps as h = 1„ (h(0),...,h(L 1))T. Intersymbol interference is avoided by assuming v ≥ L i.e. the guard interval length exceeds the duration of the channel impulse response. In the following sections, we will show that the channel is estimated from an observation r that can be written as r Ah + w, where the matrix A contains the contributions from the pilots and w can be modelled as a zero-mean Gaussian disturbance with autocorrelation matrix Rw, i.e. w N(0. Rw). The observation r given h is therefore Gaussian distributed: r|h N{Ah,Rw). The ML estimate of the channel vector h

following,

duration of

an

we assume

OFDM

—

—

=

~

~

based

on

the observation

r

is defined

as

[ 9]:

a (1) The Cramer-Rao lower bound is defined as Re h autocorrelation matrix of the estimation error e matrix J is given by [9 ] =

—

—

ĥ

J-1 ≥ 0, where Re, is the and the Fisher information

up er J times equals times times up er E Subscript r Baseline left-bracket left-parenthesi StartFraction partial-dif erential Over partial-dif erential h EndFraction ln p left-parenthesi r vertical-bar h right-parenthesi right-parenthesi Superscript plus Baseline times left-parenthesi StartFraction partial-dif erential Over partial-dif erential h EndFraction ln times p left-parenthesi r vertical-bar h right-parenthesi right-parenthesi right-bracket

(2) The MSE of

an

estimator is lower bounded

by

a

trace(J-1).

When Rw is independent from h and A the channel can easily be computed as

is invertible, the ML estimate of

ModifyingAbove h With caret Subscript up er M up er L Baseline times equals times left-parenthesi up er A Superscript plus Baseline up er R Subscript w Superscript negative 1 Baseline up er A right-parenthesi Superscript negative 1 Baseline up er A Superscript plus Baseline up er R Subscript w Superscript negative 1 Baseline r times

(3) and the MSE of the estimation is given by up er M up er S up er E times equals times up er E left-bracket double-vertical-bar h minus ModifyingAbove h With caret Subscript up er M up er L Baseline double-vertical-bar squared right-bracket equals times times t r a c e left-bracket left-parenthesis up er A Superscript plus Baseline up er R Subscript w Superscript negative 1 Baseline up er A right-parenthesis Superscript negative 1 Baseline right-bracket

(4) The MSE (4) is equal to the CRB, i.e. the estimate (3) is a minimum variance unbiased (MVU) estimate. 2.2. Cyclic Prefix OFDM perform data-aided channel estimation in CP-OFDM, some data carriers are replaced by pilot carriers. Without loss of generality, we consider the comb-type pilot arrangement [ 10]-[ 11 ]: we replace in every OFDM symbol M(≥L) data symbols To

by pilot symbols. To estimate the channel at the receiver, the N samples outside the guard interval are converted to the frequency domain. Because of the orthogonality between the carriers, data carriers do not interfere with pilot carriers. Therefore, it follows that the FFT outputs corresponding to the positions of the M pilots are not affected by the data. The M x 1 observation vector rCP of the FFT outputs at the pilot positions be written

ACP has entries where α nk denotes the v), + sqrt(N/(N (ACP)k,l αbc(nk)exp{—j2πnkl/N), index of the k-th pilot carrier, and is the bc(nk) k-th pilot symbol with energy The is Gaussian distributed with autocornoise |bc(nk)|2 wCP Es. per symbol relation matrix Rw,CP N0IM, where N0 is the spectral density of the additive white Gaussian noise and IM is the M x M identity matrix. From the orthogonality between the carriers it follows that ACP+ACP is invertible. As the autocorrelation matrix Rw,CP is independent of the vector h to be estimated, it follows that the ML channel estimate and its MSE are given by (3) and (4) with A and Rw replaced by can

as rCP

—

ACPh

+ wCP, where the M x L matrix

=

—

—

—

respectively. Hence, in CP-OFDM the ML estimate is MVU. In the that the pilot carriers are equidistant and N is a multiple of M, it can special be verified that the MSE is equal to MSE = α-2 (Es/N0)-1(L/M), i.e. the easily MSE is proportional to the number of channel taps to be estimated and inversely proportional to the number of available pilot symbols. ACP and Rw,CP case

2.3. Zero Padding OFDM Similarly as in CP-OFDM, pilot symbols in ZP-OFDM are inserted by replacing some of the data carriers by pilot carriers. The same pilot arrangement as for CPOFDM is assumed. To estimate the channel, the time-domain samples of the guard interval are added to the first ν samples of the data part of an OFDM symbol, and the resulting N samples outside the guard interval are then converted to the frequency domain by an FFT. Because of the addition of the guard interval samples to the first ν samples of the OFDM block, the orthogonality between the carriers is restored, such that the data symbols and pilot symbols do not interfere. Similarly as in CP-OFDM, the FFT outputs corresponding to the M pilot positions contain necessary and sufficient information to estimate the channel. The M x 1 vector of observations rZP can be written as rZP = AZPh + wZP, where the M x L matrix AZP has the same entries as in CP-OFDM: AZP = ACP, and the noise wZP is Gaussian distributed with autocorrelation matrix R where Fp consists of the subset of rows of the matrix F corresponding to the pilot carrier positions, F is the N x N matrix corresponding to the FFT operation, i.e. Fk,l = exp(—j2πkl/N)/sqrt{N), and the N x (N + v) matrix C corresponds to the addition of the guard interval samples to the first v samples of the OFDM block: up er C equals left-parenthesi up er I Subscript up er N Baseline times StartLayout 1st Row up er I Subscript v Baseline 2nd Row 0 Subscript left-parenthesi up er N minus v right-parenthesi x v Baseline EndLayout right-parenthesi

(5)

is independent of the channel vector h to be estimated. In the Hence, Rw,ZP that AZP+Rw,ZP-1 AZP is invertible, the ML estimate and its MSE are given and (4) by (3) respectively, by replacing A and Rw by AZP and Rw,ZP.Similarly as in CP-OFDM, the channel estimate for ZP-OFDM is MVU.

case

2.4. Known Symbol Padding OFDM In

KSP-OFDM, the v known samples

bg(k)from the guard interval can serve as pilot

symbols to estimate the channel in a data-aided way. However, the number v of guard interval samples is typically small as compared to N to keep the efficiency of the MC system

accurately estimate the channel, additional pilot symbols signal. In this paper, we assume the additional are inserted pilot symbols by replacing M v data carriers by pilot carriers, i.e. the total number of pilot symbols equals M. To estimate the channel, we start from the N + v time-domain samples from the observed OFDM block, as shown in Figure 2. The (N + v) x 1 vector rKSP of time-domain samples can be written as as

high as possible.

To

must be inserted in the MC

—

AKSPh+ wKSP. The (N + v) x L matrix AKSP contains the contributions from the pilot symbols, i.e. AKSP = AKSP,c + AKSP,g. The matrix AKSP,c contains the contributions from the pilot carriers, i.e. (AKSP,c)k,l = αsp(k l), where the rKSP

—

—

vector sp is the IFFT of the

pilot carriers only (the data carriers are set to zero), contains the contributions of the guard interval pilots, i.e. AKSP,g = where |x|N+v is the modulo-(N + v) reduction of x. (AKSP,g)k,l αbg(|k—l+v|N+v), The disturbance wKSP contains the contributions from the unknown data symbols and the additive white Gaussian noise. We have wKSP = Hsd+ wAWGN, where the vector sd is the IFFT of the data carriers only (the pilot carriers are set to zero), (H)k,l = h(k-l) and wAWGN is additive white Gaussian noise with spectral density N0. We assume the data symbols and pilot symbols transmitted on the carriers have energy per symbol Es. As the disturbance wKSP depends on the channel to be estimated through H, the derivation of the ML estimator and the true CRB are very and the matrix

complicated. As the true CRB is hard to evaluate, an approximation is made by assumthat the disturbance wKSP can be modelled as Gaussian distributed, resulting in the Gaussian Cramer-Rao bound (GCRB) [ 12], In that case, the vector rKSP given h is Gaussian distributed: rKSP|h ~ N(AKSPh, Rw,KSP), where Rw,KSP= a and Fd consists of a subset of columns of the IFFT matrix F+ corresponding to the data carrier positions. As the autocorrelation matrix Rw,KSP depends on the channel to be estimated, the following approximation is made to find an analytical expression for the GCRB: we approximate the Toeplitz matrix H by a circulant matrix which implies that we neglect the transients at the edges

ing

Figure 2. KSP-OFDM: observation interval for channel estimation

of the observed block in the contribution of the data symbols to the observation rKSP. This approximation is valid for long blocks N >> v. In that case, the matrix M) matrix Fs has HFd is equal to HFd FSHS, where the (N + v) X (N + v entries (Fs)k,l = exp(j2πknl/N)/sqrt(N), nl is the index of the l-th data carrier, and the matrix HS is a square diagonal matrix of which the diagonal elements are the outputs of the Fourier transform of the channel vector at the data carrier positions. The GCRB is then found by applying a linear transform to the vector rKSP that is based on the QR-decomposition of Fs = QX, where Q is a unitary matrix and X is an upper triangular matrix with M zero rows [12, eq 23]. Applying the linear transform Q+ to the vector rKSP yields the vector Q+ rKSP, which contains a subset of M components that is (nearly) independent of the data symbols and a subset of N + v M components that still depends on the data symbols. The subset estimator only makes use of the subset r'KSP of M components that are (nearly) data-free, where r'KSP = AKSP,sh + wKSP,s, AKSP,s and wKSP,s are respectively the parts of Q+ AKSP and Q+wK$P corresponding to the data-free subset. The subset estimator is based on the ML decision rule and is defined as [ 11 ] —

—

—

ModifyingAbove h With caret Subscript s u b s e t Baseline equals left-parenthesi up er A Subscript up er K up er S up er P comma s Superscript plus Baseline times up er A Subscript up er K up er S up er P comma s Baseline right-parenthesi Superscript negative 1 Baseline times up er A Subscript up er K up er S up er P comma s Superscript plus Baseline r prime Subscript up er K up er S up er P Baseline

(6) For finite N, the equality HFd = FSHS holds only approximately, such that practice r'KSP is affected by a residual contribution from the data symbols. This residual contribution will result in an error floor in the MSE at high Es/N0. In the above subset estimator, we applied an invertible linear transformation, independent of the channel to be estimated, to the observation vector rKSP in order to find a subset of M components that is data-free. The approximations made in the subset estimator however, resulted in a subset of M components that still contains a residual data-dependent term, which resulted in an error floor in the MSE at in

high Es/N0. To avoid the error floor at high Es/N0, the channel must be estimated v components can from a truly data-free vector. A truly data-free vector of M be found by applying an invertible linear transform that first adds the time-domain samples of the guard interval to the first v samples of the OFDM block (this restores the orthogonality between the carriers) and then converts the N resulting timedomain samples outside the guard interval to the frequency domain by means of an FFT [ 13 ]. This linear transformation is similar to the transformation used in ZP-OFDM to obtain the vector rZP, but in ZP-OFDM, this results in M datafree components corresponding to the M pilot carrier positions, whereas in KSPOFDM, this results in only M v data-free components corresponding to the M v pilot carrier positions. Hence, estimators based on this vector will be suboptimal. The vector of M v components can be written as rKSP,f = AKSP,f h+wKSP,f, where the (M —v>) x L matrix AKSP,f contains the contributions from the pilot carriers and the guard interval carriers, i.e. (AKSP,f)k,l α(bc{nk) + Bg(nk) exp(-j2πnkl/Nn)k, is the index of the k-th pilot carrier and the vector Bg is the N-point FFT of the guard interval pilots {bg(k)}. The noise contribution wKSP,f is zero-mean Gaussian distributed with autocorrelation matrix R where Fp,f —

—

—

—

=

consists of the subset of rows of the FFT matrix F corresponding to the pilot carrier positions, and C is given by (5) This autocorrelation matrix is similar to the one of ZP-OFDM, and is independent of the parameters to be estimated. The ML estimate and corresponding MSE based on the observation rKSP,j are given by (3) and (4) with A and Rw replaced by AKSP,f and Rw,KSP,f, respectively. This estimator is .

,

denoted the

frequency domain estimator.

3. Numerical Results In this

section, we evaluate the performance of the different channel estimators, 0,....,L 1, where h(0) assuming an L-tap channel with h(k) h(0)(L k), k is selected such that the channel is normalized, i.e. a with L = 8. Further, we assume the pilot symbols are BPSK modulated. The pilot carriers are randomly distributed over the spectrum and the results are averaged out over 50 =

—

=

—

randomly generated pilot positions. In Figure 3 the normalized MSE (NMSE)

and normalized CRB (NCRB), defined as NMSE = α2(Es/N0)MSE and NCRB = α2(Es/N0)CRB, are shown as function of the SNR = Es/N0. It is clear that the CP-OFDM technique outperforms all other techniques. However, the MSE performance of ZP-OFDM is close to that of CP-OFDM. At low SNR, the CRB of the KSP-OFDM technique reaches the one for CP-OFDM, whereas at high SNR, the CRB of KSP-OFDM is slightly ,

increased. Further, the MSE of the two suboptimal channel estimators for KSPOFDM, i.e. the subset estimator and the frequency domain estimator, are shown. At low SNR, the subset estimator outperforms the frequency domain estimator, but

high SNR, when the subset estimator reaches its error floor, the frequency domain estimator has a better performance. Considering Figure 3 it can be concluded that all considered channel estimators (except the subset estimator) have essentially the same performance: the difference between the curves is small. In Figure 4, the influence of the FFT size on the NMSE and NCRB is shown. It can be observed that the performance of ZP-OFDM converges to that of CP-OFDM for large N: when N >> v, the relative influence of the guard interval samples on the estimator becomes very small, such that the estimator for ZP-OFDM converges to the one of CP-OFDM. For all considered estimators, the performance is (essentially) independent of N for sufficiently large FFT size. Only at low N, the NMSE and NCRB of ZP-OFDM and KSP-OFDM (slightly ) increase with decreasing N. The influence of the number M of pilot symbols on the NMSE and NCRB is shown in Figure 5. As expected, the NMSE of the CP-OFDM technique is essentially equal to L/M, i.e. the MSE is proportional to the number of channel taps to be estimated and inversely proportional to the number of available pilots. The NMSE of ZP-OFDM is essentially equal to that of CP-OFDM. For KSP-OFDM, the NCRB and NMSE converge to the performance of CP-OFDM for large M. For small M, the NCRB and NMSE of KSP-OFDM is slightly increased as compared at

,

to

L/M.

Figure 3. Normalized CRB and MSE, ν = 7, N = 1024, M = 40

Figure 4. Influence of the FFT size N, Es/N0 = 10dB, ν = 7, M = 40

Figure 5. Influence of the number M of pilot symbols, Es/N0 = 10dB, ν = 7, N = 1024

4. Conclusions In this paper we have considered three guard interval techniques for OFDM, i.e. cyclic prefix, zero-padding and known symbol padding. For CP-OFDM and ZP-OFDM, we have derived the ML estimator for data-aided channel estimation. We have shown that the MSE of these estimators coincide with their respective Cramer-Rao bounds. For KSP-OFDM, the derivation of the ML channel estimator and the Cramer-Rao bound is very complicated. Therefore, we have presented two suboptimal ML-based estimators, i.e. the subset estimator and the frequency domain estimator, along with the Gaussian CRB. We have pointed out that CP-OFDM channel estimation outperforms the other techniques. However, the performance of the other channel estimators is close to the performance of the CP-OFDM channel estimator. The MSE and CRB turn out to be inversely proportional to the SNR (except for the subset estimator, which suffers from an error floor at high SNR) and the number of pilot symbols, and are proportional to the number of channel taps. Further, the performance of the estimators is essentially independent of the FFT size.

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C\ Taylor & Francis ~

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Distributed Space-Time Block Coding for Large Set of Relay Terminals Ryosuke UCHIDAa,1 a Department of Electrical Engineering and Computer Science, Graduate School of Engineering, Nagoya Univ., Nagoya, Japan Abstract. In this chapter, a decode-and-forward cooperative diversity scheme for wireless packet transmission network with large and undetermined set of relay terminals is considered. Correctly received signals at some relay terminals are re-transmitted to the receiver with the STBC-based cooperative relaying scheme. For large and undetermined set of relay terminals, performance of the conventional STBC-based cooperative diversity is known to be degraded due to the loss of the diversity gain and increasement of decoding complexity. This chapter discusses a signaling scheme to reduce the performance loss by introducing the linear transformation of the STBC matrix by a signature vector, which has more degrees of freedom for the assignment of signals compared to the conventional STBC-based cooperative diversity. Keywords: Wireless Telecommunications, Cooperative Communications, Cooperative Diversity, Sensor Network.

1. Introduction Cooperative diversity can achieve significant performance gain in fading channels [1]–[6]. To achieve diversity gain, orthogonal channels from relay terminals to receiver are combined at the receiver. To make multiple channels orthogonal, multiple access methods such as CDMA, TDMA, OFDMA or STBC can be employed. In this chapter, a cooperative diversity based on the STBC, which is advantageous to the other multiple access methods in its spectral efficiency, is applied to a wireless packet transmission network with large and undetermined set of relay terminals, where at any given time, only a small subset of relay terminals’ set is active and cooperates. This situation arises, for example, if decode-and-forward relaying with cyclic redundancy check (CRC) is employed at large scale wireless control/sensing network, where terminals can join or disjoin to the relay terminals’ set. In the application of the cooperative diversity based on the STBC to the wireless packet transmission network with large and undetermined set of relay terminals, there are two problems, diversity gain and complexity. For undetermined set of relay terminals, diversity gain of the cooperative diversity based on the STBC [ 1 ], [ 5 ] is

1 Corresponding Author: R. UCHIDA, Westside on Integrated Building 9th Floor, Furo-cho, Chikusa-ku, Nagoya, 464-8603, JAPAN, [email protected], http://www.katayama.nuee.nagoyau.ac.jp/~uchida/

DOI: 10.1201/9781003336853-16

Distributed Space-Time Block Coding for Large Set of Relay Terminals

known to be affected [7], [8]. When a new member is joined to the relay terminals’ set, the same column of the STBC matrix as the existing member’s may be assigned to the new relay terminal. This duplicated assignment of the same column vector causes the loss of the diversity gain. In addition to the loss of the diversity gain, increasement of decoding complexity is the second problem for the large set of relay terminals. This is because the decoding complexity of the conventional cooperative diversity is dominated by the STBC matrix size, which is proportional to the size of the relay terminals’ set. The literature on the STBC-based cooperative diversity with large and undetermined set of relay terminals is sparse. For large set of relay terminals, a cooperative signaling scheme that employs signature vectors with small size of STBC matrix is proposed in [ 9], whereas undetermined set of relay terminals is studied in [ 10]. The cooperative signaling scheme proposed in [ 9] performs joint optimization among all the members of the relay terminals’ set. Flowever, for undetermined set of relay terminals, joint optimization among all relay terminals can not be performed. Thus, in this chapter, the proposed cooperative signaling scheme in [ 10] is focused. In this scheme, random phase rotations, which can be independently determined at each relay terminal, are applied to complex values with a constant amplitude to form signature vector. Since the probability of the occurrence of duplicated signature vectors at multiple relay terminal is zero, the loss of the diversity gain can be reduced.

2. System Model In this chapter, the uplink transmission is considered. Transmission of signals from a mobile terminal (MT) to base station (BS) is performed through relay terminals (RTs). Channels between MT and RTs is distinguished from the channels between RTs and BS by employing different carrier frequencies. As discussed before, our interest is in the signaling technique at the RTs. Thus, in the following discussion, the transmission between the RTs and BS is focused. 2.1. Transmitter at Relay Terminals Each RT is equipped with single antenna and receives signals transmitted from the transmitter at the MT. The received signals for each packet of transmission data are demodulated and de-mapped based on STBC, then error detection is performed. If an error is detected, the RT does not transmit the signals to the BS, while the RT relays the signals transmitted from the MT to BS if no error is detected. In the following discussion, let us focus on the RTs where no error is detected on the received signal. Figure 1 shows the system model of the transmitter at the RT. At each RT, a transmission frame is constructed from transmission-control data such as a header and the received data packet from the MT, then mapped into a symbol sequence as x[i] ...x[I])T, (x[1] x[2] •••

2. System Model

Figure 1. Transmitter at each relay terminal

where I represents the number of symbols in each frame and T represents the transpose of the matrix. For example, x[i]∈{exp(±jπ/4), exp(±j3π/4)}, if QPSK is employed. Using the symbol sequence, the RT then generates M symbol sequences based on the orthogonal STBC for M antennas [11]. The M symbol sequences can be written as a vector: SSTBC[i]

=

(SSTBC1

[i]

SSTBC2

[i]

•••

[Si]T)BCM.

For example, if M = 2, two symbols are given by [11], [12] up erS ubscriptup erSup erTup erBup erCBaselinel ft-bracketirght-bracket qualsStarBinomialOrMatrixup erS ubscriptup erSup erTup erBup erC1Baselinel ft-bracketirght-bracketCho seup erS ubscriptup erSup erTup erBup erC2Baselinel ft-bracketirght-bracketEndBinomialOrMatrixequalsStarLayoutEnlargedleft-brace1stRow StarRo tSartFactionup erESubscriptsBaselineOver2EndFractionEndRo tSartBinomialOrMatrix left-bracketirght-bracketCho sexleft-bracketiplus1right-bracketEndBinomialOrMatrixcom a2ndRow StarRo tSartFactionup erESubscriptsBaselineOver2EndFractionEndRo tSartBinomialOrMatrixnegativexasteriskleft-bracketiplus1right-bracketCho sexasteriskleft-bracketirght-bracketEndBinomialOrMatrixcom aEndLayout

where Es is the energy of each symbol in the symbol sequence and * represents complex conjugate operation on each element of the matrix. Let us assume that the number of RTs that has correctly received signals transmitted from the MT is L. Then, all the L RTs have the same SSTBC[i]. On the cooperative relaying schemes based on STBC signaling, signal Srl [i] transmitted from the l-th RT in the i-th symbol interval can be represented as follows [9 ]: up erS ubscriptrSubSubscriptlSubscriptBaselinel ft-bracketirght-bracket quals eft-parenthesi wSubscriptl1BaselinetimeswSubscriptl2Baselinetimeselipsi wSubscriptlSubSubscriptup erMSubscriptBaselineright-parenthesi timesStarBinomialOrMatrixStarLayout1stRow StarLayout1stRow sSubscriptup erSup erTup erBup erCSubSubscript1SubscriptBaselinel ft-bracketirght-bracket2ndRow sSubscriptup erSup erTup erBup erCSubSubscript2SubscriptBaselinel ft-bracketirght-bracketEndLayout2ndRow elipsi EndLayoutCho sesSubscriptup erSup erTup erBup erCSubSubscriptup erMSubscriptBaselinel ft-bracketirght-bracketEndBinomialOrMatrixcom a

where {wl1, ··· ,wlM} represent complex weighting factors for the weighted sum of the M STBC symbol sequences. Let us assume these complex weighting factors as a vector named signature vector. Design of the signature vectors is discussed in the next section.

Signals transmitted from all the L RTs can be written as a vector: sSubscript Baselin tmeslft-bracketirght-bracket qualsStarBinomalOrMatixSartLyout1sRowStarLyout1sRowsSubscript 1Baselin eft-bracketirght-bracket2ndRowsSubscript 2Baselin eft-bracketirght-bracketEndLayout2ndRow elips EndLayoutChose Subscript Sub scriptu erLSubscriptBaselin eft-bracketirght-bracketEndBiomalOrMatixequalsStar4By Matrix1stRow1stColumnwSubscript1Sub script1SubscriptBaselin 2dColumnwSubscript1Sub script2SubscriptBaselin 3rdColumnelips 4thColumnwSubscript1Sub scriptu erMSubscriptBaselin 2dRow1stColumnwSubscript2Sub script1SubscriptBaselin 2dColumnwSubscript2Sub script2SubscriptBaselin 3rdColumnelips 4thColumnwSubscript2Sub scriptu erMSubscriptBaselin 3rdRow1stColumnelips 2ndColumnelips 3rdColumnelips 4thColumnelips 4thRow1stColumnwSubscriptu erL1Baselin 2dColumnwSubscriptu erL2Baselin 3rdColumnelips 4thColumnwSubscriptu erLSub scriptu erMSubscriptBaselin EdMatrixSartBinomalOrMatixSartLyout1sRowStarLyout1sRowsSubscriptu erSuperTuperBuperCSub script1SubscriptBaselin eft-bracketirght-bracket2ndRowsSubscriptu erSuperTuperBuperCSub script2SubscriptBaselin eft-bracketirght-bracketEndLayout2ndRow elips EndLayoutChose Subscriptu erSuperTuperBuperCSub scriptu erMSubscriptBaselin eft-bracketirght-bracketEndBiomalOrMatixcom aequals perWuperS ubscriptu erSuperTuperBuperCBaselin eft-bracketirght-bracket om a

where W represents weight matrix whose (l, m)-th element is wlm. Signals (Sr1[i], ··· ,SrL[i])T generated at the L RTs are then simultaneously transmitted to the BS with the same carrier frequency. The frequency for transmission from the RTs to BS is assumed to be different from that for transmission from MT to RTs. In the transmission to BS from each RT, symbol timing is assumed to be synchronized to the other RTs’. 2.2. Channel between Relay Terminals and Base Station Signals re-transmitted from the L RTs are fluctuated due to the multipath fading and then received at the BS. Let us assume that the number of antennas at the BS is 1, then received signal in the i-th symbol interval, r[i], is given as follows: rleft-bracketirght-bracketequalsleft-parenthesi b1timesb2timeselipsi bSubscriptup erLBaselineright-parenthesi timesStartBinomialOrMatrixStartLayout1stRow StartLayout1stRow up erS ubscriptr1Baselineleft-bracketirght-bracket2ndRow up erS ubscriptr2Baselineleft-bracketirght-bracketEndLayout2ndRow elipsi EndLayoutCho seup erS ubscriptrSubSubscriptup erLSubscriptBaselineleft-bracketirght-bracketEndBinomialOrMatrixtimesplusnleft-bracketirght-bracketcom a

where bl represents the channel between the l-th RT and the BS. bl is a complex random variable and assumed to be constant value during a frame interval and changes independently in a different frame interval, n [i] denotes noise sample at the BS in the i-th symbol interval and is assumed to be independently and identically (i.i.d.) distributed complex Gaussian random variable with mean zero and variance N0.

Based on the fact that all the L RTs have the same transmission data to the BS. Signal flow from the RTs to BS can be illustrated as Figure 2. From the figure, received signal r[i] at the BS is given by rleft-bracketirght-bracketequalsbSuperscriptup erTBaselinetimesup erWsSubscriptup erSup erTup erBup erCBaselinel ft-bracketirght-bracketplusnleft-bracketirght-bracketcom aequalshSuperscriptup erTBaselinesSubscriptup erSup erTup erBup erCBaselinel ft-bracketirght-bracketplusnleft-bracketirght-bracketcom a

where h is a product of the channel b and weight matrix W as follows: StartBinomialOrMatrix StartLayout 1st Row h 1 2nd Row elipsi EndLayout Cho se h Subscript up er M Baseline EndBinomialOrMatrix equals h equals up er W b Superscript up er T Baseline period

Figure 2. Signal flow between the transmitter and receiver through relay terminals

2.3. Base Station At the BS, the received signals for each transmitted data frame are demodulated and de-mapped based on STBC by employing the estimates of the channel information h. Ideal estimation of the channel information h at the BS is assumed here. The symbols after de-mapping is denoted by {y[l], y[2],.... y[i],.... y[I]}. Then, if M 2, y[2i] =

and y[2i + 1]

are StartBinomialOrMatrix y left-bracket 2 i right-bracket Cho se y left-bracket 2 i plus 1 right-bracket EndBinomialOrMatrix equals Start 2 By 2 Matrix 1st Row 1st Column h 1 asterisk 2nd Column h 2 2nd Row 1st Column h 2 asterisk 2nd Column negative h Subscript 1 Baseline EndMatrix times StartBinomialOrMatrix r left-bracket 2 i right-bracket Cho se r asterisk left-bracket 2 i plus 1 right-bracket EndBinomialOrMatrix period

The symbols {y[1],y[2],...,y[i],...,y[I]} are then ML detected and the estimates of the transmitted symbols or, thus, the input data to the transmitter at the MT is obtained.

3. Design of the Signature Vectors In this section, design of the signature vectors, or complex weight matrix W,is discussed. For unknown set of relay terminals, signature vector is independently determined at each relay terminal. Let us begin with the two constraints on the weight matrix W. One of the constraints concerns on the total transmission power: In comparison of various weight matrices, total power should be constant. average power of the signal sr[i] transmitted from the RTs is: up er E Subscript s Baseline equals up er E left-bracket s Subscript r Superscript up er H Baseline left-bracket i right-bracket s Subscript r Baseline left-bracket i right-bracket right-bracket equals up er E left-bracket s Subscript up er S up er T up er B up er C Superscript up er H Baseline left-bracket i right-bracket up er W Superscript up er H Baseline times up er W s Subscript up er S up er T up er B up er C Baseline left-bracket i right-bracket right-bracket comma

where E [·] denotes ensemble average. The right-hand side of the above equation can be rewritten as: up erEleft-bracketsSubscriptup erSup erTup erBup erCSuperscriptup erHBaselinel ft-bracketirght-bracket imesup erWSuperscriptup erHBaselineup erWsSubscriptup erSup erTup erBup erCBaselinel ft-bracketirght-bracketright-bracket qualsup erEleft-bracket rleft-parenthesi sSubscriptup erSup erTup erBup erCSuperscriptup erHBaselinel ft-bracketirght-bracket imesup erWSuperscriptup erHBaselineup erWsSubscriptup erSup erTup erBup erCBaselinel ft-bracketirght-bracketright-parenthesi right-bracketcom aequalstrleft-parenthesi up erWup erEleft-bracketsSubscriptup erSup erTup erBup erCBaselinel ft-bracketirght-bracketsSubscriptup erSup erTup erBup erCSuperscriptup erHBaselinel ft-bracketirght-bracketright-bracketup erWSuperscriptup erHBaselineright-parenthesi period

If the each element of sSTBC[i] is assumed to be uncorrelated, thus normalup erEleft-bracketnormalsSubscriptup erSup erTup erBup erCBaselineleft-bracketirght-bracketnormalsSubscriptup erSup erTup erBup erCSuperscriptup erHBaselineleft-bracketirght-bracketright-bracketequalsStartFractionup erESubscriptsBaselineSubscriptBaselineOverup erMEndFraction ormalup erISubscriptup erMBaselinecom a

and the first constraint on the weight matrix W is given as: normal t normal r times left-parenthesi up er W up er W Superscript up er H Baseline right-parenthesi times equals times normal t normal r times left-parenthesi up er W Superscript up er H Baseline up er W right-parenthesi times equals times StartAbsoluteValue up er W EndAbsoluteValue Subscript up er F Superscript 2 Baseline equals up er M comma

where |·|F denotes Frobenius norm of the matrix. The other constraint concerns on the diversity order. Let us consider a W that provides maximum diversity gain on the assumption that each element of the channel b is independent and L ≥ M. At the receiver, signal-to-noise ratio (SNR) after the de-mapping based on STBC is given as: gam aSubscriptup erSup erTup erBup erCBaselinetimesStartFractionup erESubscriptsBaselineSubscriptBaselineOverup erMup erN0EndFractionStartAbsoluteValuehEndAbsoluteValuesquaredequalsStartFractionup erESubscriptsBaselineSubscriptBaselineOverup erMup erN0EndFraction ormalup erSigmaUnderscriptmequals1Overscriptup erMEndscriptstimesStartAbsoluteValuehSubscriptmBaselineEndAbsoluteValuesquaredperiod

The aim of diversity is to reduce the probability that the SNR YSTBC goes to low level. From the above equation, this is achieved by summing more numbers of independent random variables |hm|2s. Thus the weight matrix should be determined to make |hm|2s uncorrelated.

From the above discussion, maximum diversity gain is achieved when the each element of h is independent. Independent hm can be obtained if the weight matrix W satisfies WT E[bbH] WHW E[hhH] IM =

=

=

Thus if WHW = IM, then the maximum diversity gain is obtained. 3.1. Random Selection In conventional cooperative relaying schemes based on the direct assignment of the column vector of the STBC matrix, equivalent weight matrix for RTs is determined as follows: 1. 2. 3. 4. 5.

For each row vector of W,apply2to4. Choose one element from the row vector. Set 1 to the element. Set 0 to the other elements. Multiply W by √M/L.

Let us call the above weighting scheme as “random selection.” The resulting weight matrix W satisfies power constraint, however, it sometimes does not satisfy the condition for the diversity order.

For example, if M = L = 2, four possible patterns of the weight matrix W is normal up er W el ment-of StartSet Start 2 By 2 Matrix 1st Row 1st Column 1 2nd Column 0 2nd Row 1st Column 1 2nd Column 0 EndMatrix com a Start 2 By 2 Matrix 1st Row 1st Column 1 2nd Column 0 2nd Row 1st Column 0 2nd Column 1 EndMatrix com a Start 2 By 2 Matrix 1st Row 1st Column 0 2nd Column 1 2nd Row 1st Column 1 2nd Column 0 EndMatrix com a Start 2 By 2 Matrix 1st Row 1st Column 0 2nd Column 1 2nd Row 1st Column 0 2nd Column 1 EndMatrix EndSet period

The four patterns are equally probable, with the probability of 1/4, since two RTs independently determine corresponding rows of the weight matrix. If the weight matrix W corresponds to the first or last pattern, there is no diversity gain. Thus, maximum

diversity

order

can not

be obtained with the

probability

of 1/2.

3.2. Random Rotation As discussed above, maximum diversity order can be achieved by choosing the weight matrix W that satisfies WHW = IM. This is not completely achieved as long as each RT independently determines corresponding signature vector of the weight matrix. However, the probability that W which satisfies WHW ~ IM can be increased. To increase the probability, random rotation scheme, of which weight matrix is given as the following equation, can be employed [10]: normalup erWtimes qualstimesStarRo tSartFaction1Overup erLEndFractionE dRo t imesStar 4By4Matrix1stRow1stColumnexpleft-parenthesi jBaselin 2piup erXSubscriptu imes1 Baselin right-parenthesi 2ndColumnexpleft-parenthesi jBaselin 2piup erXSubscriptu imes12Baselin right-parenthesi 3rdColumn elips 4thColumnexpleft-parenthesi jBaselin 2piup erXSubscriptu imes1up erMBaselin right-parenthesi 2ndRow1stColumnexpleft-parenthesi jBaselin 2piup erXSubscriptu imes21Baselin right-parenthesi 2ndColumnexpleft-parenthesi jBaselin 2piup erXSubscriptu imes2 Baselin right-parenthesi 3rdColumn elips 4thColumnexpleft-parenthesi jBaselin 2piup erXSubscriptu imes2up erMBaselin right-parenthesi 3rdRow1stColumn elips 2ndColumn elips 3rdColumn elips 4thColumn elips 4thRow1stColumnexpleft-parenthesi jBaselin 2piup erXSubscriptu imesup erLBaselin 1Baselin right-parenthesi 2ndColumnexpleft-parenthesi jBaselin 2piup erXSubscriptu imesup erLBaselin 2Baselin right-parenthesi 3rdColumn elips 4thColumnexpleft-parenthesi jBaselin 2piup erXSubscriptu imesup erLup erMBaselin right-parenthesi EndMatrixcom a

where Xulm is a uniform distributed random variable whose range is [0, 1]. The weight matrix is changed frame by frame and remains constant in the same frame duration.

From the above equation, it is clear that all the diagonal elements of WHW is 1, while the other elements becomes sum of the complex random variables with the same amplitude 1/L and random arguments which uniformly distribute on the range [0, 2π]. Thus if L is enough large, WHW can be approximated by IM and the maximum diversity gain can be expected.

4. Numerical Examples In this section, frame-error performance of the weighting schemes are evaluated by Monte-Carlo simulations. On the performance evaluations, the transmission from the RTs to BS is focused. Fading environment is assumed to be modeled as Rayleigh fading environment, thus, bls are assumed to be i.i.d. complex Gaussian random variables with mean zero and variance 1. This is the worst-case scenario, in which multipath reflected waves have comparable strength to that of the direct wave [13].

Figure 3. Average frame-error rate (M = 2)

4.1. Average Frame-Error RateM=wit2 h Figure 3 shows the average frame-error performance of the random rotation and 256 QPSK symbols, number random selection schemes. In this figure, frame size I of STBC symbol sequences M 2, and number ofRTs L =1, 2, and 3 is assumed. —

=

The horizontal axis of the figure corresponds with the average. In addition to the result with random rotation and random selection schemes, the result with the optimum weight matrix that achieves maximum diversity is also shown with the label “ideal assignment."

From the figure, it can be noted that the two curves for the random rotation and random selection schemes with L = 1 shows the same performance. L = 1 means that there is only one RT that transmits the signal to the BS. Thus no weight matrix can achieve spatial diversity order of M = 2 since the channel is single-input single output. If the number of the RTs L ≥ 2, the random rotation scheme shows better performance compared to the random selection scheme with the same L. Since the gradients of the curves of the random rotation scheme to SNR are steeper than those of the random selection scheme, the performance difference of the two schemes becomes larger as SNR becomes larger. With L = 3 RTs, the random rotation scheme shows the best performance among these six curves without “ideal assignment.” If the random rotation scheme is compared to random selection at FER = 10−3 and L = 3, the difference of the performance of two schemes is about 5 [dB]. However, when it is compared with “ideal assignment” performance, there is a performance loss of 2 [dB].

5. Concluding Remarks In this chapter, cooperative relaying based on STBC is considered. For large unknown set of relay terminals, diversity order of the random selection cooperative

relaying schemes is shown to be decreased due to duplicated mapping of the same column vector of the STBC matrix to multiple RTs. On the contrary, random phase rotation scheme decreases the probability of the occurrence of the signaling pattern that decreases diversity order.

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A Comparison Between Parametric and Nonparametric Channel Estimation for Multipath Fading Channels Dieter Van Welden1, Frederik Simoens, Heidi Steendam and Marc Moeneclaey Ghent University, Gent, Belgium Abstract. This paper makes a comparison between parametric and nonparametric channel estimation in multipath fading channels. For both estimation methods, a theoretical lower bound for the MSE on the received symbol pulse is derived. This lower bound is based on the Cramer-Rao bound. We show that by optimizing the number of parameters to estimate, the MSE can be minimized. Simulation results show that the parametric estimation method has the best performance. Keywords: Multipath Fading Channels, Channel Estimation, Cramer-Rao Bound.

1. Introduction In wireless communication systems the channel is frequency-selective, because of signal reflections caused by obstacles in the environment. Those reflections generate intersymbol interference (ISI) at the receiver. The conventional way to solve this problem is through equalization of the received signal. The equalizer needs an accurate estimate of the received symbol pulse in order to counter the ISI. In this contribution the channel is modeled as multipath Rayleigh fading. We consider two channel estimation strategies: i) a parametric channel estimation method which estimates the path gains and delays of the multipath channel and computes the samples of the received symbol pulse based on these estimates; ii) a nonparametric channel estimation method which estimates the samples of the received symbol pulse without exploiting the multipath structure. It has been indicated that the parametric channel estimation method improves the estimation accuracy [1,2,3]. We investigate the two estimation methods by examining the resulting mean squared error (MSE) on the received symbol pulse. We derive an MSE lower bound based on the Cramer-Rao lower bound (CRB). Our theoretical results are confirmed by simulation results.

1 Corresponding Author: Dieter Van Welden, Sint-Pietersnieuwstraat 41, 9000 Gent, Belgium. E-mail: [email protected]

DOI: 10.1201/9781003336853-17

A Comparison Between Parametric and Nonparametric Channel Estimation

2. System Model We consider a channel with impulse response hchannel (t). A data sequence {a(k)} is transmitted over the channel using a band limited transmit pulse p(t) with bandwidth B. The received symbol pulse h(t) is defined as the convolution of the transmit pulse and the channel impulse response h times left-parenthesi t right-parenthesi equals integral Subscript minus infinity Superscript plus infinity Baseline p times left-parenthesi t minus tau right-parenthesi h Subscript c normal h normal a normal n normal n e Baseline 1 Baseline times left-parenthesi tau right-parenthesi d times tau times

A number of K pilot symbols {a(k), k = 0,...,K— 1} with |a(k)|2 = Es, are transmitted over the channel to enable channel estimation at the receiver. The corresponding received signal r(t) is given by r left-parenthesi t right-parenthesi equals left-parenthesi t right-parenthesi plus w left-parenthesi t right-parenthesi equals normal up er Sigma Underscript k equals 0 Overscript up er K minus 1 Endscripts a times left-parenthesi k right-parenthesi times h left-parenthesi t minus k up er T right-parenthesi plus w left-parenthesi t right-parenthesi

(1)

where s(t) represents the useful signal and w(t) is zero-mean complex-valued white Gaussian noise with power spectral density N0.

3. Channel Estimation Strategies This section is devoted to the estimation of the received symbol pulse h(t). First the parametric channel estimation method is explained and afterwards the nonparametric estimation method is treated. 3.1. Parametric Channel Estimation In the parametric strategy, it is assumed that h(t) corresponds to some parametric model h0(t; x) which depends on a set of Npar real-valued parameters x =[x(1),...,x(Npar)]T, where [.]T denotes transposition. For h0(t; x), we consider a multipath model: h 0 times left-parenthesi t imes emicol n normal x right-parenthesi equals normal up er Sigma Underscript l equals 0 Overscript up er L minus 1 Endscripts alpha Subscript l Baseline times p times left-parenthesi t minus tau Subscript l Baseline right-parenthesi

(2) where p(t) is the transmit pulse, L denotes the number of paths, {αl} and {τl} denote the gains and the delays, respectively, and x consists of the path delays and the real and imaginary parts of the path gains. Hence, h0(t; x) is characterized by Npar = 3L real parameters.

3. Channel Estimation Strategies

Assuming that h(t) = h0(t; x) for some value of x, the received signal r(t) is r(t)= s0(t; x) + w(t)(3)

where s0(t; x) denotes the useful component up er S 0 left-parenthesi t imes semicolon normal x right-parenthesi equals normal up er Sigma Underscript k equals 0 Overscript up er K minus 1 Endscripts a left-parenthesi k right-parenthesi h Subscript 0 Baseline left-parenthesi t minus k up er T semicolon normal x right-parenthesi

(4) Since we consider pilot aided channel estimation, the receiver knows the structure of s0(t; x) The maximum-likelihood (ML) estimate of x based on the observation model (3) is defined as ModifyingAbove normal x With caret equals arg min Underscript normal x Endscripts integral StartAbsoluteValue r left-parenthesis t right-parenthesis minus up er S 0 left-parenthesis t imes semicolon normal x right-parenthesis EndAbsoluteValue squared d t

(5) The samples of the received symbol pulse are computed by using this ML estimate, according to (6) ModifyingAbove h With caret imes Overscript Endscripts left-parenthesi m times up er T Subscript s Baseline right-parenthesi equals h 0 left-parenthesi m up er T Subscript s Baseline times emicol n ModifyingAbove normal x With caret right-parenthesi

where Ts is the sampling period. In order to avoid aliasing the sampling rate 1/Ts should satisfy 2BTs ≤ 1. In practice, the received symbol pulse h(t) only approximately satisfies the model (2): no value of x exists for which the equality h(t) = h0(t; x) holds. Instead, we define x0 as the value of x which results in the best fit for h0(t; x) according to the following criterion normal x 0 equals arg times min Underscript normal x Endscripts integral StartAbsoluteValue h left-parenthesis t right-parenthesis minus h 0 left-parenthesis t times semicolon normal x right-parenthesis EndAbsoluteValue squared d t times

(7) The vector x0 is unknown by the receiver and has to be estimated. We will consider the estimator from (5) but with r(t) satisfying (1) instead of (3). Finally, using the estimate X resulting from (5), the estimate of the received pulse will be obtained according to (6). 3.2. Nonparametric Channel Estimation The nonparametric channel estimation method estimates the samples of the received 1, without using the underlying channel strucsymbol pulse h(mTs), with 2BTS ture. As h(t) is bandlimited, its duration is infinite. Hence, in practice only a finite ≤

number of samples h(mTs) can be estimated. We will estimate the samples h(mTs) for which m is in the predefined range [—L1Ts, L2Ts], which results in N L1 + L2 + 1 samples to be estimated. The samples of the received symbol pulse h(t) and the received signal r(t) can be grouped in Ns T/Ts vectors hi and ri respectively =

=

(i=

1,......,Ns) hi =[h(—L1Ts + (i— 1)Ts), h(—(L1Ts + T + (i— 1)Ts),...]T ri =[r(—L1Ts + (i — 1)Ts), r(—L1Ts + T + (i— 1)Ts),...]T

where hi has Ni entries so that hjNi. If we to a duration NTS, we can write each vector ri as ri

=

Aihi,

assume

that h(t) is time-limited

+ wi (8)

1) × Ni Toeplitz matrix with first column (K + Ni and wi is the noise vector; the noise vectors wiand wi' [a(0)... a(K 1)01×Ni—1]T are independent when i≠i'. The ML estimate of hi based on the observation model (8) is given by [4 ]

where Ai is

a

pilot-dependent

—

—

ModifyngAbovenormalhWithcaretSubscriptiBaselineSubscriptBaseline quals eft-parenthesi normalup erASubscriptiSuperscriptup erHBaselineSubscriptSuperscriptBaselinenormalup erASubscriptiBaselineSubscriptBaselineright-parenthesi Superscriptnegative1Baselinenormalup erASubscriptiSuperscriptup erHBaselinerSubscriptiBaselinetimes

(9) where [.]H denotes the Hermitian operator. In practice h(t) is not time-limited to a duration of N sampling intervals, so we will consider the estimate (9) but with ri based on the true observation model (1).

4. MSE on the Received Symbol Pulse h(t) The MSE on the received symbol pulse is used as a measure to compare the accuracy of the two estimation methods. This MSE is defined as up er M up er S up er E equals normal up er E left-bracket integral Subscript minus infinity Superscript plus infinity Baseline StartAbsoluteValue h left-parenthesis t right-parenthesis minus ModifyingAbove h With caret left-parenthesis t right-parenthesis EndAbsoluteValue squared d t right-bracket

(10) where E[.] denotes the expectation over all possible pilot sequences and over the noise. Note that this MSE also holds for a fixed pseudo-random pilot sequence of sufficient length. For both estimation methods we derive a theoretic lower bound on the MSE. 4.1. Parametric Channel Estimation For the parametric channel estimation method the MSE (10) is defined as up er M up er S up er E equals normal up er E left-bracket integral Subscript minus infinity Superscript plus infinity Baseline StartAbsoluteValue h left-parenthesis t right-parenthesis minus h 0 left-parenthesis t imes semicolon ModifyingAbove normal x With caret right-parenthesis EndAbsoluteValue squared d t right-bracket

(11) For high Es/N0 it can be shown that h0(t; x) is an asymptotically unbiased estimate of h0(t; x0), so the MSE (11) can be decomposed as up er M up er S up er E equals integral Subscript minus infinity Superscript plus infinity Baseline StartAbsoluteValue h left-parenthesis t right-parenthesis minus h 0 left-parenthesis t imes semicolon normal x Subscript 0 Baseline right-parenthesis EndAbsoluteValue squared d t plus normal up er E left-bracket integral Subscript minus infinity Superscript plus infinity Baseline StartAbsoluteValue h 0 left-parenthesis t imes semicolon ModifyingAbove normal x With caret right-parenthesis minus h 0 left-parenthesis t imes semicolon normal x 0 right-parenthesis EndAbsoluteValue squared d t right-bracket

(12) The first and second term of (12) are caused by the modeling error h(t) — h0(t; x0) and the estimation error x — x0, respectively. The second term in (12) can

be lower bounded by the CRB corresponding to the observation model (3). This yields the following lower bound on the total MSE (see appendix A) up er M up er S up er E greater-than-or-equal-to integral Subscript minus infinity Superscript plus infinity Baseline StartAbsoluteValue h left-parenthesi t right-parenthesi minus h 0 left-parenthesi t semicolon normal x Subscript 0 Baseline right-parenthesi EndAbsoluteValue squared d t plus StartFraction up er N 0 up er N Subscript normal p normal a r Baseline Over 2 up er K up er E Subscript up er S Baseline EndFraction

(13) This MSE lower bound consists of two parts: a first part caused by the modeling and a second part caused by the additive noise. We see that the second term is proportional to the number Npar of estimated parameters. error

4.2. Nonparametric channel estimation For the nonparametric channel estimation method, the MSE (10) on the received symbol pulse can be rewritten as up er M up er S up er E equals up er T Subscript up er S Baseline normal up er E left-bracket normal up er Sigma Underscript m equals negative infinty Overscript plus infinty Endscripts StartAbsoluteValue h left-parenthesi m up er T Subscript s Baseline right-parenthesi minus ModifyingAbove h times With caret left-parenthesi m up er T Subscript s Baseline right-parenthesi EndAbsoluteValue squared right-bracket

(14) As already mentioned before, h(mTs) is only estimated for —L1 ≤ m ≤ L2 so h(mTs) = 0 outside that range. Hence, (14) reduces to up erMup erSup erEequalsup erTSubscriptnormalsBaselinenormalup erSigmaUnderscriptmnot-an-el ment-ofleft-bracketminusup erL1timescom aup erL2right-bracketEndscriptsUnderUnderscriptUnderUnderUnderscriptEndscriptsStartAbsoluteValuehleft-parenthesi mup erTSubscriptnormalsBaselineright-parenthesi EndAbsoluteValuesquaredplusup erTSubscriptnormalsBaselinenormalup erEleft-bracketnormalup erSigmaUnderscriptmequalsminusup erL1Overscriptup erL2EndscriptsStartAbsoluteValuehleft-parenthesi mup erTSubscriptnormalsBaselineright-parenthesi minusModifyingAbovehWithˆleft-parenthesi mup erTSubscriptnormalsBaselineright-parenthesi EndAbsoluteValuesquaredright-bracket

(15) When the duration of the actual pulse h(t) exceeds NTs, the first part of (15) denotes a modeling error. The second part is caused by estimation errors and can again be lower bounded by the CRB, corresponding to the observation model (8) (see appendix B). The total MSE (15) is lower bounded as up er M up er S up er E greater-than-or-equal-to up er T Subscript s Baseline normal up er Sigma Underscript m not-an-el ment-of left-bracket minus up er L 1 times com a up er L 2 right-bracket Endscripts StartAbsoluteValue h left-parenthesi m up er T Subscript s Baseline right-parenthesi EndAbsoluteValue squared plus StartFraction up er N 0 times 2 up er N Over 2 up er K up er E Subscript up er S Baseline EndFraction

(16)

As 2N is the number estimated real-valued parameters, the second term of (16) is proportional to the number of estimated parameters. We observe that both expressions (13) and (16) have a similar structure: the first and second term are caused by the modeling error and additive noise, respectively. This modeling error is caused by the difference between h(t) and h0(t; x0) for the parametric estimation method, and by the duration of h(t) exceeding NTs for the nonparametric method.

5. Numerical Results In this section the obtained theoretical results are illustrated by some numerical results and the two estimation methods are compared.

Figure 1. Influence of the number of estimated paths on the MSE for parametric channel estimation

We consider a multipath fading channel with 3 paths. We assume that the first path delay τ0 is uniformly distributed in (0,T ) and the delay differences, τ1 — τ0 and τ2— τ0, are uniformly distributed in (0, 4T). Rayleigh fading is assumed so the channel gains αl are complex-valued Gaussian random variables with zero mean and variance 1/3. As transmit pulse a square root raised cosine pulse with 25% roll-off is used. The pilot sequence consists of 20 BPSK symbols. The sample period Ts is set to T/2 to avoid aliasing. The MSE results displayed are averaged over the statistics of the path delays, path gains, pilot sequences and noise. The simulation results for the parametric estimation method are shown in figure 1, while figure 2 shows the simulation results for the nonparametric estimation method. The solid lines correspond to the theoretical lower bound on the total MSE while the dashed lines correspond to the simulation results obtained from an actual channel estimator. For the parametric estimation method, the ML estimate (5) is too complex to compute because it involves an L-dimensional search [5]. To reduce the computational complexity, an estimation method based on the iterative SAGE algorithm [6] is used instead. The theoretical results are confirmed by the simulation results. We observe for both estimation methods that the modeling error causes an MSE floor at large Es/No. By increasing the number of estimated parameters this modeling error can be reduced but at the same time the noise-dependent term of the MSE is increased. Elence, the MSE can be minimized for each value of Es/N0 by optimizing the number of parameters to be estimated. In figure 3 the theoretical lower bound for the nonparametric estimation method is shown as a function of the number of estimated coefficients of the received l0dB. The contributions caused by the modsymbol pulse {h(mTs)} for Es/N0 error and the noise also shown separately. A number of 16 estimated are eling by channel coefficients results in a minimum of the lower bound on the total MSE. =

Figure 2. Influence of the number of estimated taps on the MSE for nonparametric channel estimation

Figure 3. Influence of the number of estimated taps on the total MSE lower bound for Es/N0 = 10dB

The horizontal line in figure 3 corresponds to the lower bound for the parametric estimation method with L = 3. We can see that the MSE lower bound for the nonparametric estimation method exceeds the MSE lower bound for parametric estimation with L = 3.

6. Conclusion We have made a comparison between parametric and nonparametric channel estimation for multipath fading channels in terms of the MSE on the received symbol pulse. The MSE consists of two terms, caused by the modeling error and the estimation error, respectively. For both methods we derived the respective Cramer-Rao lower bound on the part of the MSE caused by the estimation error. The influence of the number of estimated paths for the parametric estimation method and the number of estimated channel taps for the nonparametric estimation method was investigated. We have shown that for every Es/N0 the number of parameters to be estimated can be optimized so that the MSE is minimized. Finally we have observed that the nonparametric estimation method is outperformed by the parametric estimation method in terms of the MSE on the received symbol pulse.

Appendix A The second term in (12) is lower bounded by the corresponding Cramer Rao Lower bound (CRB) [7] normalup erEleft-bracketinegralSubscriptminusinf itySuperscipt lusinf ityBaselineStarAbsoluteValueh0left-parenthesi t imes emicol nModifyngAbovenormalxWithˆright-parenthesi minush0left-parenthesi t imes emicol n ormalx0right-parenthesi EndAbsoluteValuesquared tvertical-barStarSetaleft-parenthesi kright-parenthesi EndSetright-bracketgreater-than-orequal-tonormalup erEleft-bracketinegralSubscriptminusinf itySuperscipt lusinf ityBaselineGermanup erRleft-bracenormalv eft-parenthesi tright-parenthesi Supersciptnormalup erHBaselineup erCup erRup erBleft-parenthesi normalx0right-parenthesi normalv eft-parenthesi tright-parenthesi rght-bracedtvertical-barStarSetaleft-parenthesi kright-parenthesi EndSetright-bracket

(17) where CRB(x0) is the inverse of the Fischer information matrix Jp related to the estimation of x0 and normalvleft-parenthesi tright-parenthesi equals eft-bracketStartFractionpartial-difer ntialh0left-parenthesi tsemicol nModifyngAbovenormalxWithcaretright-parenthesi Overpartial-difer ntialModifyngAbovenormalxWithcaretEndFractionright-bracketSubscriptModifyngAbovenormalxWithcaretequalsnormalx0

Jp is defined as [8] normalup erJSubscriptnormalpBaseline qualsStartFraction2Overup erN0EndFractionintegralGermanup erRleft-braceleft-bracketStartFractionpartial-difer ntialsSubscript0Baselineleft-parenthesi tsemicol nup erXright-parenthesi Overpartial-difer ntialup erXEndFractionright-bracketSubscriptnormalxequalsnormalx0Baselineleft-bracketStartFractionpartial-difer ntialsSubscript0Baselineleft-parenthesi tsemicol nup erXright-parenthesi Overpartial-difer ntialup erXEndFractionright-bracketSubscriptnormalxequalsnormalx0Superscriptnormalup erHBaselineright-bracedt imes

Averaging (17) over the pilot symbols gives rise to normalup erESubscriptSartSe aleft-parenthesi kright-parenthesi EndSetBaselinel ft-bracketinegralSubscriptminusinf itySuperscipt lusinf ityBaselineGermanup erRleft-bracenormalv eft-parenthesi tright-parenthesi Supersciptnormalup erHBaseline ormalup erJSubscriptnormalpSupersciptnegative1Baseline ormalv eft-parenthesi tright-parenthesi rght-bracedtright-bracket qualsnormaltnormalr eft-parenthesi ntegralSubscriptminusinf itySuperscipt lusinf ityBaselineGermanup erRleft-bracenormalv eft-parenthesi tright-parenthesi normalv eft-parenthesi tright-parenthesi Supersciptnormalup erHBaselineright-bracedtnormalup erESubscriptSartSe aleft-parenthesi kright-parenthesi EndSetBaselinel ft-bracketnormalup erJSubscriptnormalpSupersciptnegative1Baselineright-bracketright-parenthesi

(18) where tr(.) denotes the trace.

We apply to (18) Jensen’s inequality for matrices [9] because the inverse of a matrix is a matrix convex function normalup erESubscriptStartSetaleft-parenthesi kright-parenthesi EndSetBaselineleft-bracketnormalup erJSubscriptnormalpSuperscriptnegative1Baselineright-bracketgreater-than-or-equal-toleft-parenthesi normalup erESubscriptStartSetaleft-parenthesi kright-parenthesi EndSetBaselineleft-bracketnormalup erJSubscriptnormalpBaselineright-bracketright-parenthesi Superscriptnegative1

Averaging Jp over the pilot symbols yields normal up er E Subscript StartSet a left-parenthesi k right-parenthesi EndSet Baseline left-bracket normal up er J Subscript normal p Baseline right-bracket equals StartFraction 2 up er K up er E Subscript up er S Baseline Over up er N 0 EndFraction integral German up er R left-brace normal v left-parenthesi t right-parenthesi normal v left-parenthesi t right-parenthesi Superscript normal up er H Baseline right-brace d t

(19) so expression (18) is lower bounded by StartFraction up er N 0 Over 2 up er K up er E Subscript up er S Baseline EndFraction t r left-parenthesi integral Subscript minus infinty Superscript plus infinty Baseline German up er R left-brace normal v left-parenthesi t right-parenthesi normal v left-parenthesi t right-parenthesi Superscript normal up er H Baseline right-brace d t left-bracket integral Subscript minus infinty Superscript plus infinty Baseline German up er R left-brace normal v left-parenthesi t right-parenthesi normal v left-parenthesi t right-parenthesi Superscript normal up er H Baseline right-brace d t right-bracket Superscript negative 1 Baseline right-parenthesi

(20) This yields for (20)

StartFractionup erN0Over2up erKup erESubscriptup erSBaselineEndFraction ormaltnormalrleft-parenthesi up erISubscriptup erNSubSubscriptparSubscriptBaselineright-parenthesi equalsStartFractionup erN0up erNSubscriptnormalpnormalarBaselineOver2up erKup erESubscriptup erSBaselineEndFraction

where Im is the m × m identity matrix.

Appendix B The second term of (15) can be rewritten as up erTSubscriptup erSBaselineup erEtimesleft-bracketnormalup erSigmaUnderscriptmequalsminusup erL1Overscriptup erL2EndscriptsStartAbsoluteValuehtimesleft-parenthesi mtimesup erTSubscriptup erSBaselineright-parenthesi minusModifyngAbovehWithcaretleft-parenthesi mtimesup erTSubscriptup erSBaselineright-parenthesi EndAbsoluteValuesquaredright-bracketequalsup erTSubscriptsBaselinenormalup erSigmaUnderscriptiequals1Overscriptup erNSubscriptsBaselineEndscriptsup erEleft-bracketStartAbsoluteValuenormalhSubscriptiBaselineSubscriptBaselineminusModifyngAbovenormalhSubscriptiBaselineWithcaretSubscriptBaselineEndAbsoluteValuesquaredright-bracket

(21) Every term of the summation is lower bounded by the CRB up erTSubscriptsBaselinenormalup erSigmaUnderscriptmequalsminusup erL1Overscriptup erL2Endscriptsnormalup erEleft-bracketStartAbsoluteValuenormalhSubscriptiBaselineSubscriptBaselineminusModifyngAbovenormalhSubscriptiBaselineWithcaretSubscriptBaselineEndAbsoluteValuesquaredright-bracketgreater-than-or-equal-toup erTSubscriptup erSBaselinetimestrtimesleft-parenthesi up erJSubscriptnpiSuperscriptnegative1Baselineright-parenthesi

(22) where Jnpi is the corresponding Fischer information matrix. The Fischer information matrix is in this case a well-known result [8] normaluperJSubscriptnormaln ormalptimesiBaselin equalsStarF ction2uperTSubscriptu erSBaselin OveruperN0EndFractionStar2By2Detrminat1sRow1stColumnGermanuperRleft-parenthsi normaluperASubscriptSupersciptBaselin Subscript Supersciptu erHBaselin ormaluperASubscript Baselin SubscriptBaselin rght-parenthsi 2ndColumn iusModifyngAboveuperSWith lde ft-parenthsi normaluperASubscriptSupersciptBaselin Subscript Supersciptu erHBaselin ormaluperASubscript Baselin SubscriptBaselin rght-parenthsi 2ndRow1stColumn perSoverTilde ft-parenthsi normaluperASubscriptSupersciptBaselin Subscript Supersciptu erHBaselin ormaluperASubscript Baselin SubscriptBaselin rght-parenthsi 2ndColumnGermanuperRleft-parenthsi normaluperASubscriptSupersciptBaselin Subscript Supersciptu erHBaselin ormaluperASubscript Baselin SubscriptBaselin rght-parenthsi EndDetrminat

(23) This yields up erTSubscriptup erSBaselinenormalup erSigmaUnderscriptmequalsminusup erL1Overscriptup erL2Endscriptsnormalup erEleft-bracketStartAbsoluteValuenormalhSubscriptiBaselineSubscriptBaselineminusModifyngAbovenormalhSubscriptiBaselineWithcaretSubscriptBaselineEndAbsoluteValuesquaredright-bracketgreater-than-or-equal-toup erN0normalup erSigmaUnderscriptiequals1Overscriptup erNSubscriptsBaselineEndscriptsnormaltnormalr eft-parenthesi left-parenthesi Germanup erRleft-bracketnormalup erASubscriptiSuperscriptnormalup erHBaselinenormalup erASubscriptiBaselineSubscriptBaselineright-bracketright-parenthesi Superscriptnegative1Baselineright-parenthesi

(24)

Averaging this result over the pilot symbols and applying Jensen’s inequality for matrices [9] results in up erTSubscriptup erSBaselinenormalup erSigmaUnderscriptmequalsminusup erL1Overscriptup erL2Endscriptsnormalup erEleft-bracketSartAbsoluteValuenormalhSubscriptiBaselineSubscriptBaselineminusModifyngAbovenormalhWithcaretSubscriptiBaselineSubscriptBaselineEndAbsoluteValuesquaredright-bracketgreater-than-orequal-toup erN0normalup erSigmaUnderscriptiequals1Overscriptup erNSubscriptup erSBaselineEndscriptsStarFactionup erNSubscriptiBaselineOverup erKup erESubscriptup erSBaselineEndFraction

(25) which

be further

can

simplified using the fact

that

Ni

as

up erTSubscriptup erSBaselinenormalup erSigmaUnderscriptmequalsminusup erL1Overscriptup erL2Endscriptsnormalup erEleft-bracketStartAbsoluteValuehSubscriptiBaselineminusModifyngAbovenormalhSubscriptiBaselineWithcaretSubscriptBaselineEndAbsoluteValuesquaredright-bracketgreater-than-or-equal-toStartFractionup erN02up erNOver2up erKup erESubscriptup erSBaselineEndFraction

(26)

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Envelope Correlation Analysis of MRC Signals in Correlated Rician Fading Zhuwei Wang, Xin Zhang Beijing University of Posts and Telecommunications Beijing, P. R. China growing attention of channel correlation for high channel correlation introducing severe performance degradation, the correlation property of signals has been a hotpot in the research process of mobile communication systems. In this section, considering the noise and channel estimation error, we analyze the envelope correlation coefficient (ECC of the maximal ratio combining (MRC) output over correlated Rician fading channels, then

Abstract. With the

compare the characters of ECC in different environments. Besides, we also derive the system performance such as average capacity and outage probability. Finally, we present the relation between the ECC and system performance in the stationary environment. It is interesting that the relation becomes simpler because ECC can replace the impacts of Rician factor and channel attenuation of each path.

Keywords Correlated Rician fading channel. Envelope correlation coefficient, Performance, Maximal ratio combining.

1. Correlated Raleigh Fading Consider a general frequency diversity system with single path in correlated Rayleigh fading channel. The complex channel gain at carrier frequency fk can be expressed as hk xk+ jyk = 1, 2(1) =

k

where xk and yk denote the real and imaginary parts of the scatter components with zero-mean Gaussian random variables and variance k . We will study the correlation properties of two signals at frequencies f1 and f2. We can obtain the relation between components of signals as follows [1] up erEleft-bracketx1timesx2right-bracket imesequalsup erEleft-brackety1timesy2right-bracketequalsStartFractionsigma1times igma2timesup erJ0left-parenthesi 2pifSubscriptmBaselinetauright-parenthesi Over1plusleft-parenthesi 2pinormalup erDeltaftauSubscriptrmsBaselineright-parenthesi squaredEndFractionup erEleft-bracketx1timesy2right-bracket imesequalsminusup erEleft-bracketx2timesy1right-bracketequalsminus2pinormalup erDeltaftauSubscriptrmsBaselineup erEleft-bracketx1timesx2right-bracket

(2) where fm and Τ represent the maximal Doppler shift and time delay. J0(·) is the zeroth order Bessel function of the first kind. And Δf and Τrms denote the frequency separation and the root mean square (rms) delay spread, respectively. E[·] is expectation operation.

The envelopes of two signals are defined by r 1 times equals times StartRo t x 1 squared plus y 1 squared EndRo t r 2 times equals times StartRo t x 2 squared plus y 2 squared EndRo t

(3)

DOI: 10.1201/9781003336853-18

Envelope Correlation Analysis of MRC Signals in Correlated Rician Fading

Figure 1. ECC versus time delay in correlated Rayleigh fading channels

Then the envelope correlation coefficient (ECC) can be obtained by [1]: rho prime times StartFraction up er C o v left-bracket r 1 comma r 2 right-bracket Over StartRo t v a r left-bracket r 1 right-bracket v a r left-bracket r 2 right-bracket EndRo t imes EndFraction equals StartFraction up er J 0 squared left-parenthesi 2 pi f Subscript m Baseline tau right-parenthesi Over 1 plus left-parenthesi 2 pi normal up er Delta f tau Subscript r m s Baseline right-parenthesi squared EndFraction

(4) We can see that ECC of the signals is influenced by the maximal Doppler shift, frequency separation, time delay and rms delay spread. A similar plot based on Eq. (4) is shown in Figure 1 for rms delay spread is 0.25 ‫מ‬s at 900MHz. From Figure 1 we can find that the ECC decreases as the frequency separation becomes larger. In addition, the ECC is waved with the time delay. ,

2. Correlated Rician Fading 2.1. Envelope Correlation Coefficient Analysis We will analyze the ECC between two MRC signals considering the noise and channel estimation error (CEE) in correlated Rician fading channel. In the diversity system with L resolvable paths at each carrier, we add the line of sight (LOS) components to Eq. (1) and the complex channel gain on the lth path at carrier fk can be expressed as hk,l

-

(ak,l + xk,l)

+

j(bk,l +

yk,l)

k

= 1, 2, l

=

(5) L 1, 2, ...,

2. Correlated Rician Fading where the LOS components are ak,l and bk,l, and the scatter components are xk,l and yk,l with mean value 0 and variance a . Without loss of generality, all fading

paths of each carrier

are

assumed to be normalized

so

that

E

.

In correlated muti-path Rician fading channels, the correlation properties of scatter components can be deduced from Eq. (2): covleft-bracketxSubscriptk1Baselin com al1timescom axSubscriptk2Baselin com al2right-bracket qualscovtimeslft-bracketySubscriptk1Baselin com al1timescom aySubscriptk2Baselin com al2right-bracket quals0covleft-bracketxSubscriptk1Baselin com al1timescom aySubscriptk2Baselin com al2right-bracket quals0timescom afor-al 1not-equals 2covleft-bracketxSubscript1com alBaselin com axSubscript2com alBaselin right-bracket qualscovleft-bracketySubscript1com alBaselin com aySubscript2com alBaselin right-bracket qualsStarFactionsigmaSubscript1com alBaselin times igmaSubscript2com alBaselin timesuperJ0left-parenthesi 2pifSubscriptmBaselin tauright-parenthesi Over1timespluseft-parenthesi 2pinormaluperDeltaf uSbscript msBaselin right-parenthesi quaredEndFractionequalsmuSbscriptlBaselin covleft-bracketxSubscript1com alBaselin com aySubscript2com alBaselin right-bracket qualsnegativecovleft-bracketySubscript1com alBaselin com axSubscript2com alBaselin right-bracket qualsminus2pinormaluperDeltaf uSbscript msBaselin muSbscriptlBaselin k1com ak2times quals1timescom a2timescom altimescom al1com al2equals1timescom a2timescom aseparto cm auperL

(6)

Considering the noise and CEE, we can write the received signals as y Subscript k comma l Baseline times equals StartRo t up er P Subscript up er S Baseline EndRo t imes up er S h Subscript k comma l Baseline plus StartRo t up er P Subscript up er N Baseline EndRo t imes n Subscript k comma l Baseline plus StartRo t up er P Subscript up er E Baseline EndRo t imes e Subscript k comma l Baseline

(7) where nk,l and ek,l represent the normalized noise and CEE, and PS, PN and PE denote the average signal, noise and error power, respectively. S is the transmitted signal with constant envelope modulation, namely |S|= 1. Then, the maximal ratio combining signal at carrier fk can be given by [2] r Subscript k Baseline quals normal up er Sigma Underscript l equals 1 Overscript up er L Endscripts times StartRo t up er P Subscript up er S Baseline EndRo t imes up er S StartAbsoluteValue h Subscript k com a l Baseline EndAbsoluteValue squared plus normal up er Sigma Underscript l equals 1 Overscript up er L Endscripts left-parenthesi StartRo t up er P Subscript up er N Baseline EndRo t imes n Subscript k com a l Baseline plus StartRo t up er P Subscript up er E Baseline EndRo t imes e Subscript k com a l Baseline right-parenthesi h Subscript k com a l Superscript asterisk

(8) the superscript (·)* denotes conjugate. In Eq. (8), the former term is the available signal and the latter one is the mixed noise. In the high SNR region, it is high possibility that the envelope of noise is much smaller than that of the desired signal, which means up er P left-brace vertical-bar normal up er Sigma Underscript l equals 1 Overscript up er L Endscripts StartRo t up er P Subscript up er S Baseline EndRo t up er S StartAbsoluteValue h Subscript k com a l Baseline EndAbsoluteValue squared much-les -than StartAbsoluteValue normal up er Sigma Underscript l equals 1 Overscript up er L Endscripts times left-parenthesi StartRo t up er P Subscript up er N Baseline EndRo t imes n Subscript k com a l Baseline plus StartRo t up er P Subscript up er E Baseline EndRo t imes e Subscript k com a l Baseline right-parenthesi h Subscript k com a l Superscript asterisk Baseline EndAbsoluteValue right-brace 1

(9) where P{·} denotes the probability function. We use an proved method: when a > 0 and |b| Then the envelope of rk can be given by

α,

we

have |a + b| ≈ α+ Re{b}.

StarAbsoluteValuerSubscriptkBaselin EndAbsoluteValue qualsStarAbsoluteValuerSubscriptkBaselin up erSasteriskEndAbsoluteValue qualsStarAbsoluteValuenormalup erSigmaUndersciptlequals1Oversciptup erLEndscripts imesStarRo tup erPSubscriptup erSBaselin EndRo t imesStarAbsoluteValuehSubscriptkcom alBaselin EndAbsoluteValuesquaredplusnormalup erSigmaUndersciptlequals1Oversciptup erLEndscripts imesl ft-parenthesi StarRo tup erPSubscriptup erNBaselin EndRo tnSubscriptkcom alBaselin plusStarRo tup erPSubscriptup erEBaselin EndRo teSubscriptkcom alBaselin right-parenthesi hSubscriptkcom alSupersciptaseriskBaselin up erSasteriskEndAbsoluteValuealmost-equalsnormalup erSigmaUndersciptlequals1Oversciptup erLEndscripts imesStarRo tup erPSubscriptup erSBaselin EndRo t imesStarAbsoluteValuehSubscriptkcom alBaselin EndAbsoluteValuesquaredplus p erReStarSetnormalup erSigmaUndersciptlequals1Oversciptup erLEndscripts imesl ft-parenthesi StarRo tup erPSubscriptup erNBaselin EndRo tnSubscriptkcom alBaselin plusStarRo tup erPSubscriptup erEBaselin EndRo teSubscriptkcom alBaselin right-parenthesi hSubscriptkcom alSupersciptaseriskBaselin up erSasteriskEndSet

(10)

Due to the independence between hk,l, nk,l and ek,l, the later part of Eq. (10) is a zero mean random value with the variance (PE + PN) a , which is independent with the former part of the formula. The ECC of two MRC signals can be expressed as rhotimesequalstimesStartFractionup erCovtimesleft-parenthesi StartAbsoluteValuer1EndAbsoluteValuecom aStartAbsoluteValuer2EndAbsoluteValueright-parenthesi OverStartRo tup erVarleft-parenthesi StartAbsoluteValuer1EndAbsoluteValueright-parenthesi timesup erVarleft-parenthesi StartAbsoluteValuer2EndAbsoluteValueright-parenthesi EndRo tEndFraction

(11) Substituting Eq. (6) and Eq. (10) into Eq. (11), we get that rhotimes qualsStarFaction ormalup erSigmaUndersciptlequals1Oversciptup erLEndscripts imesup erPSubscriptup erSBaselin muS bscriptlBaselin timesl ft-bracketup erJ0left-parenthesi 2pifSubscriptmBaselin tauright-parenthesi gmaSubscript1com alBaselin times igmaSubscript2com alBaselin timesplusaSubscript1com alBaselin timesaSubscript2com alBaselin plusbSubscript1com alBaselin timesbSubscript2com alBaselin timesplus2pinormalup erDeltaftauS bscriptrmsBaselin timesl ft-parenthesi bSubscript1com alBaselin timesaSubscript2com alBaselin minusaSubscript1com alBaselin timesbSubscript2com alBaselin right-parenthesi rght-bracketOvernormalup erPiUndersciptkequals1Overscipt2EndscriptsStarRo tup erPSubscriptup erSBaselin ormalup erSigmaUndersciptlequals1Oversciptup erLEndscripts imes igmaSubscriptkcom alSuperscipt2Baselin left-parenthesi gmaSubscriptkcom alSuperscipt2Baselin plusaSubscriptkcom alSuperscipt2Baselin plusbSubscriptkcom alSuperscipt2Baselin right-parenthesi plusone- ight left-parenthesi up erPSubscriptup erNBaselin plus p erPSubscriptup erEBaselin right-parenthesi normalup erSigmaUndersciptlequals1Oversciptup erLEndscriptsleft-parenthesi 2sigmaSubscriptkcom alSuperscipt2Baselin plusaSubscriptkcom alSuperscipt2Baselin plusbSubscriptkcom alSuperscipt2Baselin right-parenthesi EndRo tEndFraction

(12) stationary environment, corresponding paths have the identical statistical characteristic [3][4]. Namely, a1,l σ2,l σl and al, b1,l a2,l b2,l blσ1,l Τ 0. Then Eq. (12) can be simplified to In the

—

=

=

=

=

=

=

rho times equals times left-parenthesi beta xi times left-parenthesi 2 up er K plus 1 right-parenthesi normal up er Sigma Underscript l equals 1 Overscript up er L Endscripts times alpha Subscript l Superscript 4 Baseline right-parenthesi slash left-parenthesi StartFraction left-parenthesi up er K plus 1 right-parenthesi squared Over 2 EndFraction plus xi left-parenthesi 2 up er K plus 1 right-parenthesi normal up er Sigma Underscript l equals 1 Overscript up er L Endscripts times alpha Subscript l Superscript 4 Baseline right-parenthesi

(13)

(2πΔfτrms)2).

where β ξ K and αl denote average signal-to-noise ratio 1/ (1 + Rician factor and channel attenuation (SNR), coefficient, respectively. These parameters are defined as =

xiequalsup erPSubscriptu perSBaselin slahleft-parenthesi up erPSubscriptu perNBaselin plus p erPSubscriptu perEBaselin right-parenthesi up erKequalseft-parenthesi aSubscriptlSuperscipt2Baselin plusbSubscriptlSuperscipt2Baselin right-parenthesi lash2sigmaSubscriptlSuperscipt2Baselin alphaSubscriptlSuperscipt2Baselin equals2 igmaSubscriptlSuperscipt2Baselin plusaSubscriptlSuperscipt2Baselin plusbSubscriptlSuperscipt2

left-parenthesis 14 right-parenthesis

From the Eq. (14), we can find that the noise and CEE have the same impact on the ECC. If we eliminate them, the ECC can be given by rho times equals times StartFraction 1 Over 1 times plus times left-parenthesis 2 pi normal upper Delta f tau Subscript r m s Baseline right-parenthesis squared EndFraction

(15) For the stationary environment, Eq. (15) equals the ECC provided in [3]–[5]. Besides, we can see that the ECC of MRC signals is the same as the ECC in the correlated Rayleigh fading channel. We plot the Figure 2 to compare the ECC in different situations. We can clear see that CEE and noise reduce the ECC in the stationary environment. When ignore the CEE and noise, the ECC in correlated Rician fading channels is the same as that in correlated Rayleigh fading channels.

Figure 2. ECC versus frequency separation in different situations

2.2. Performance In this section, we will analyze the system performance over correlated Rician fading channels. Then we will figure out the relation between the system performance and ECC.

2.2.1. Capacity We define the channel gain vector h

=

[h1,1, h1,2,

. . .,

h1, L,h.2,1L](16)

The elements of the vector

are complex Gaussian random variables, which can CN2L (vh, Rh). vhand Rh denote the mean vector and covariance matrix, respectively. In particular, vh is just the complex LOS components. Then the channel capacity is given by [6 ]

be expressed as h

~

C

=

log2 (1

+

ξhHh)

bits/s/Hz(17)

the superscript (·)H denotes Hermitian transposition.

Based on [6], we can obtain the expression of average channel capacity over correlated Rician fading channels as follows up er E left-parenthesis up er C right-parenthesis almost-equals log Subscript 2 Baseline left-parenthesis c right-parenthesis minus StartFraction 1 Over ln 2 EndFraction left-parenthesis StartFraction 1 Over q EndFraction plus StartFraction 1 Over 3 q squared EndFraction minus StartFraction 2 Over 1 5 q Superscript 4 Baseline EndFraction right-parenthesis

(18) where qequalscsquaredslashdcequals1plusxitmesleft-parenthesi tracetimesup erRSubscripthBaselinetimesplusvSubscripthSuperscriptup erHBaselinevSubscripthBaselineright-parenthesi dequalsStartFractionxisquaredOver2EndFractionleft-parenthesi tracetimesup erRSubscripthSuperscript2Baselinetimesplus2vSubscripthSuperscriptup erHBaselinetimesup erRSubscripthBaselinevSubscripthBaselineright-parenthesi

(19)

In the stationary environment, using Eq. (6) and Eq. (16), we can get up er E left-parenthesis up er C right-parenthesis times equals times log Subscript 2 Baseline left-parenthesis 1 times plus times 2 xi right-parenthesis minus StartFraction 1 Over ln 2 EndFraction left-parenthesis StartFraction 1 Over q EndFraction plus StartFraction 1 Over 3 q squared EndFraction minus StartFraction 2 Over 15 q Superscript 4 Baseline EndFraction right-parenthesis

(20) where q times equals times left-parenthesis 1 times plus times 2 xi right-parenthesis squared times left-parenthesis 1 plus up er K right-parenthesis squared slash left-parenthesis xi squared left-parenthesis 2 up er K plus times 1 right-parenthesis times left-parenthesis 1 times plus times beta right-parenthesis normal up er Sigma Underscript l equals 1 Overscript up er L Endscripts alpha Subscript l Superscript 4 Baseline right-parenthesis

(21) Based on Eq. (13) and Eq. (20), we can deduce the relationship between ECC and the average capacity. The parameter q in Eq. (21) can be expressed by ECC as q

=

2(l

+

2ξ)2 (β-ρ)/ξρ(l+β)(22)

It is obvious from Eq. (22) that the relation between ECC and the average capacity is simple and the influence of K and αlare replaced by that of ρ. Figure 3 shows the relation between ECC and average capacity with rms delay spread is 0.25 μs and SNR is 8dB. It can be easily observed that the average capacity is a fixed monotone decreasing function of ECC in stationary environments. Besides, the average capacity tends to be affected more severely with the ECC increasing. 2.2.2. Outage Probability We define

m Subscript k times comma l Baseline times equals times left-parenthesis StartRo t up er P Subscript up er N Baseline EndRo t n Subscript k comma l Baseline times plus times StartRo t up er P Subscript up er E Baseline EndRo t e Subscript k comma l Baseline right-parenthesis slash StartRo t up er P Subscript up er N Baseline plus times up er P Subscript up er E Baseline EndRo t

(23) We can assume that the vector m =[m1,1,m1,2, ···,m1,L,m2,1,m2,2, ···,

m2,L] follows the joint 2L -dimensional zero-mean complex circular Gaussian distribution with covariance matrix Rm = I. Based on Eq. (8), the SNR of the MRC signals is given by gam a times equals times StartFraction xi left-parenthesi normal h Superscript up er H Baseline normal h right-parenthesi squared Over left-parenthesi normal h Superscript up er H Baseline normal m right-parenthesi left-parenthesi normal h Superscript up er H Baseline normal m right-parenthesi Superscript up er H Baseline EndFraction

(24)

Figure 3. Average capacity versus ECC in correlated Rician channels

Based on [7], we can obtain the outage probability of MRC signals over correlated Rician fading channels: up er P Subscript normal o normal u normal t Baseline equals StartFraction 1 Over det left-parenthesi normal up er I plus normal up er Lamda normal up er R Subscript normal h Baseline right-parenthesi EndFraction exp left-parenthesi minus v Subscript h Superscript up er H Baseline normal up er R Subscript normal h Superscript negative 1 Baseline v Subscript h Baseline times plus times v Subscript h Superscript up er H Baseline normal up er R Subscript h Superscript negative 1 slash 2 Baseline left-parenthesi up er I times plus normal up er Lamda normal up er R Subscript normal h Baseline right-parenthesi normal up er R Subscript normal h Superscript negative 1 slash 2 Baseline v Subscript h Baseline right-parenthesi

(25) where

signal to noise protection ratio. In the stationary environment, substituting Eq. (6) and Eq. (16) into Eq. (25): g

ξ/g

=

,

g

the

up erPSubscriptnormalon rmalunormaltBaseline qualsnormalup erPiUnderscipt equals1Oversciptup erLEndscripts imesStarFaction1Over1plustimes4normalup erLamdasigmaSubscript Superscipt2Baselineplustimes4left-parenthesi 1minusbetaright-parenthesi normalup erLamdasquaredsigmaSubscript Superscipt4BaselineEndFractiontimes xpleft-bracketnormalup erSigmaUndersciptjequals1Oversciptup erLEndscriptsStarFaction4up erKnormalup erLamdasigmaSubscriptjSuperscipt2Baselinel ft-parenthesi 2left-parenthesi betaminus1right-parenthesi normalup erLamdasigmaSubscriptjSuperscipt2Baselineminus1right-parenthesi Over1timesplustimes4normalup erLamdasigmaSubscriptjSuperscipt2Baselinetimesplustimes4left-parenthesi 1minusbetaright-parenthesi normalup erLamdasquaredsigmaSubscriptjSuperscipt4BaselineEndFractionright-bracket

(26)

be

In a general system, we simplified as

assume

ct

1.

Using Taylor formula, Eq. (26) can

up er P Subscript normal o normal u normal t Baseline times equals times left-parenthesis 1 minus StartFraction 2 normal up er Lamda Over 1 times plus times up er K EndFraction right-parenthesis times exp left-bracket minus 2 normal up er Lamda plus StartFraction 2 up er K normal up er Lamda squared left-parenthesis 1 times plus beta right-parenthesis Over left-parenthesis 1 plus up er K right-parenthesis squared EndFraction normal up er Sigma Underscript j equals 1 Overscript up er L Endscripts alpha Subscript j Superscript 4 Baseline right-bracket

(27)

Figure 4. Outage probability versus ECC in correlated Rician channels Based on (13) and (27) as follows

,

we can

get the relationship between ECC and the outage

probability

up er P Subscript normal o normal u normal t Baseline times equals times left-parenthesis 1 minus StartFraction 2 normal up er Lamda Over 1 times plus times up er K EndFraction right-parenthesis times exp left-bracket minus 2 normal up er Lamda times plus StartFraction rho normal up er Lamda squared left-parenthesis 1 times plus times beta right-parenthesis Over 2 xi left-parenthesis beta minus rho right-parenthesis EndFraction times right-bracket

(28) The influence of αlin Eq. (27) are also replaced by that of ρ. Figure 4 demonstrates outage performance versus ECC with rms delay spread is 0.25 µs and Rician factor K = 20. We can find that the outage probability is a monotone increasing function of ECC in logarithmic y-axis. Besides, the outage performance tends to be affected by ECC more severely in lower outage probability environments.

References [1] W. C. Jakes, Ed., Microwave Mobile Communications. New York : IEEE Press, 1974. [2] J. G. Proakis, Digital Communications, third ed., New York: Mc Graw Hill, 1995. [3] Y. Karasawa and H. Iwai , “Modeling of signal envelope correlation of line-of-sight fading with applications to frequency correlation analysis”, IEEE Transactions on Communications, vol. 42, no. 6, pp. 2201–2203, June 1994. [4] J. R. Mendes and M. D. Yacoub, “Power correlation coefficient of a general fading mode”, IEEE MTT-S International Conference, pp. 497– 502, July 2005. [5] Zhuwei Wang, Yanfen Hu , Xubin Chen, Xin Zhang and Dacheng Yang, “Analytical envelope correlation and outage probability of maximal-ratio combined rician fading channels,” Proceedings IEEE VTC Fall Conference, pp. 926–930, October 2007.

[6] Q. T. Zhang and D. P. Liu, “A simple capacity formula for correlated diversity rician fading channels”, IEEE communication letters, vol. 6, no. 11, November 2002. [7] X. W. Cui , Q. T. Zhang, and Z. M. Feng, “Outage probability for maximal ratio combining of arbitrarily correlated faded signals corrupted by multiple Rayleigh interferers ,” IEEE Transactions Vehicular Technology, vol. 55, no. 1, pp. 383–386, January 2006.

C\ Taylor & Francis ~

Taylor&FrancisGroup http://taylo ra ndfra n ci s.com

Experimental Investigation of Channel Estimation for IEEE802.11b WLAN System Yu Imaoka , Hiroshi Obata, Yohei Suzuki, and Yukitoshi Sanada1 Dept. of Electronics and Electrical Engineering, Keio University, Yokohama, Japan Abstract. In the IEEE802.11b WLAN standard, direct-sequence / spread-spectrum (DS/SS) modulation is employed. With a fractional sampling RAKE receiver, it is possible to achieve diversity and reduce the BER in DS/SS communication. In order to realize the diversity through fractional sampling, an impulse response of the channel must be estimated. In this chapter, a channel estimation scheme for the IEEE802.11b WLAN system is presented through experiment. In order to estimate the impulse response of the channel, a pseudoinverse matrix with a threshold is employed. Numerical results indicate that the channel can be estimated precisely with an optimum threshold. Keywords: Channel estimation, IEEE802.11b, Pseudo-inverse matrix, DS/SS, Experimental investigation.

1. Introduction Various wireless communication systems have been implemented such as mobile phones, wireless LANs, etc. IEEE802.1lb WLAN is one of the popular broadband communication standards and is employed all over the world. In the IEEE802.11b WLAN standard, direct-sequence spread-spectrum (DS/SS) is used as a modulation scheme. In DS/SS systems, a RAKE receiver is employed to improve the signal-tonoise ratio (SNR) in a multipath environment and achieve path diversity. The effect of tap spacing on the performance of the DS/SSRAKE receiver is analyzed [ 1 ]—[ 3 ], If the tap spacing is narrower than the chip duration, the performance can be improved by using a combining rule based on a maximum-likelihood criterion. In order to decide the tap positions of the RAKE receiver, channel estimation is required. There are many literatures on channel estimation for CDMA systems [4]—[6]. However, most of them are not applicable to a RAKE receiver with fractional sampling. In this chapter, a channel estimation scheme for the IEEE802.11b WLAN receiver with fractional sampling is presented. In the conventional scheme, the impulse response of a multipath channel is estimated with a pseudo-inverse of an auto-correlation matrix of a received signal waveform [7]. However, this scheme is not robust to thermal noise. Therefore, the pseudo-inverse matrix with a threshold

1 Yukitoshi Sanada, 3-14-1 Hiyoshi, Kohoku, Yokohama, Kanagawa, 223-8522 Japan. E-mail: [email protected] URL: http://www.snd.elec.keio.ac.jp

DOI: 10.1201/9781003336853-19

Experimental Investigation of Channel Estimation is proposed [3 ], The threshold is introduced to suppress the influence of the noise. The proposed scheme is evaluated through experiment. The measurement with the IEEE802.1lb WLAN card is compared with that of the Vector Network Analyzer and the mean square errors (MSE) of the estimated channel responses are presented.

This chapter is organized as follows. In Section 2, the conventional and proposed schemes are explained. Section 3 shows the measurement results. Section 4 gives our conclusions.

2. Channel Estimation Schemes 2.1. Estimation with an Inverse Matrix Here, the chip shape is assumed to be rectangular. At the beginning of the packet, NSy synchronization symbols are transmitted. The synchronization symbol, s(t),is represented as, s(t)

= ds(t)c(t)(1)

where ds(t) is the transmitted symbol and c(t) is the spreading sequence, and d Subscript s Baseline Subscript Baseline left-parenthesis t right-parenthesis equals normal up er Sigma Underscript n equals 0 Overscript up er N Subscript up er S y Baseline minus 1 Endscripts d left-parenthesis n right-parenthesis p times left-parenthesis t minus n up er T Subscript s Baseline Subscript Baseline right-parenthesis comma

(2) c left-parenthesis t right-parenthesis equals ModifyingAbove normal up er Sigma With infinity Underscript m equals minus infinity Endscripts c Subscript b Baseline left-parenthesis times m mod up er M right-parenthesis times q times left-parenthesis t minus m times up er T Subscript c Baseline right-parenthesis

(3) where p(t) is the signal waveform, and q(t) is the chip waveform. cb(m) is the mth spreading sequence, d(n) is the nth symbol for synchronization, Ts is the symbol duration, Tc is the chip duration, and M is the length of the spreading sequence. Therefore, MTc = Ts. The influence of the multipath can be modeled by a transversal filter as shown in Figure 1. {h0,h1,...,hL—1} is the impulse response of the channel and L is the number of the paths. The received signal is given as r left-parenthesis t right-parenthesis equals normal up er Sigma Underscript l equals 0 Overscript up er L minus 1 Endscripts h Subscript l Baseline s times left-parenthesis t minus l up er T Subscript d Baseline right-parenthesis plus n left-parenthesis t right-parenthesis

(4) where hl is the response of the lth path, n(t) is the thermal noise, and Td is the interval of the samples. Here, N times oversampling is assumed, and NTd = Tc.If the received signal is sampled with the interval of Td, the kth sample of the received signal, rs(k), is expressed as r Subscript Baseline Subscript s Baseline left-parenthesi k right-parenthesi equals normal up er Sigma Underscript l equals 0 Overscript up er L minus 1 Endscripts h Subscript l Baseline s times left-parenthesi left-parenthesi k minus l right-parenthesi times up er T Subscript d Baseline right-parenthesi plus n Subscript s Baseline Subscript Baseline left-parenthesi k right-parenthesi equals normal s Superscript up er T Baseline normal h plus n Subscript Baseline Subscript s Baseline left-parenthesi k right-parenthesi

(5)

2. Channel Estimation Schemes

Figure 1. Transversal filter

where ns(k) is the kth noise sample. h and s aregiven as h

=

[h0,h1,....,hL—1]T,(6) s(k) =

[s(kTd),s((k(7)—1—()Td),.d)Ls](Tk

The received signal is input into a matched filter. The output of the matched filter is x left-parenthesi k right-parenthesi equals normal up er Sigma Underscript m equals 0 Overscript up er M Subscript s Baseline minus 1 Endscripts c Subscript Baseline Subscript s Baseline left-parenthesi m right-parenthesi times r Subscript s Baseline Subscript Baseline times left-parenthesi m minus k right-parenthesi period

(8) The auto-correlation function of the spreading sequence is uSubscriptBaselineSubscriptsBaselineleft-parenthesi kright-parenthesi equalsnormalup erSigmaUnderscriptmequals0Overscriptup erMSubscriptsBaselineminus1EndscriptstimescSubscriptBaselineSubscriptsBaselineleft-parenthesi mright-parenthesi timescSubscriptBaselineSubscriptsBaselineleft-parenthesi mminuskright-parenthesi

(9) where cs(m) is the mth coefficient of the matched filter. Ms = MN represents the number of samples for one spreading sequence. cs(m) is given by sampling c(t) with the interval of Td. An example of auto-correlation of the waveform is shown in Figure 2. From Eq. (5), the output of the matched filter is derived as xleft-parenthesi kright-parenthesi equalsnormalup erSigmaUnderscriptmequals0Overscriptup erMSubscriptsBaselineminus1EndscriptscSubscriptBaselineSubscriptsBaselinel ft-parenthesi mright-parenthesi timesrSubscriptBaselineSubscriptsBaselinetimesleft-parenthesi mminuskright-parenthesi equalsnormalup erSigmaUnderscriptmequals0Overscriptup erMSubscriptsBaselineminus1EndscriptscSubscriptsBaselineSubscriptBaselinel ft-parenthesi mright-parenthesi timesStartSetnormalup erSigmaUnderscriptlequals0Overscriptup erLminus1EndscriptshSubscriptlBaselinestimesleft-parenthesi left-parenthesi mminuskminuslright-parenthesi up erTSubscriptdBaselineright-parenthesi plusnSubscriptsBaselineSubscriptBaselinetimesleft-parenthesi mminuskright-parenthesi EndSet

(10) equalsnormalup erSigmaUnderscriptlequals0Overscriptup erLminus1EndscriptsequalstimesStartSetnormalup erSigmaUnderscriptmequals0Overscriptup erMSubscriptsBaselineminus1EndscriptscSubscriptsBaselineSubscriptBaselineleft-parenthesi mright-parenthesi times timesleft-parenthesi left-parenthesi mminuskminuslright-parenthesi up erTSubscriptdBaselineright-parenthesi EndSethSubscriptlBaselineplusnormalup erSigmaUnderscriptmequals0Overscriptup erMSubscriptsBaselineminus1EndscriptscSubscriptsBaselineSubscriptBaselineleft-parenthesi mright-parenthesi timesnSubscriptsBaselineSubscriptBaselinetimesleft-parenthesi mminuskright-parenthesi period

(11) Assuming that ds(t) = 1 in Eq. (1), s((m

—

k

l)

—

Td)

=

cs(m

—

k

—

l).(12)

Figure 2. Auto-correlation of the spreading sequence

Therefore, xleft-parenthesi kright-parenthesi equalsnormalup erSigmaUndersciptlequals0Oversciptup erLminus1Endscripts imesStarSetnormalup erSigmaUndersciptmequals0Oversciptup erMSubscriptsBaselin minus1EndscriptscSubscriptsBaselin left-parenthesi mright-parenthesi tmesctimesl ft-parenthesi left-parenthesi m inuskminuslright-parenthesi up erTSubscriptdBaselin right-parenthesi EndSethSubscriptlBaselin plusnormalup erSigmaUndersciptmequals0Oversciptup erMSubscriptsBaselin minus1EndscriptscSubscriptsBaselin left-parenthesi mright-parenthesi tmesnSubscriptsBaselin timesl ft-parenthesi m inuskright-parenthesi equalsnormalup erSigmaUndersciptlequals0Oversciptup erLminus1EndscriptsuS bscriptsBaselin timesl ft-parenthesi kminuslright-parenthesi tmeshSubscriptlBaselin plusnormalup erSigmaUndersciptmequals0Oversciptup erMSubscriptsBaselin minus1EndscriptscSubscriptsBaselin left-parenthesi mright-parenthesi tmesnSubscriptsBaselin timesl ft-parenthesi m inuskright-parenthesi equalsnormaluS bscriptsSupersciptup erTBaselin left-parenthesi kright-parenthesi tmesnormalhplusnSubscriptcBaselin left-parenthesi kright-parenthesi

where

n Subscript c Baseline left-parenthesi k right-parenthesi equals normal up er Sigma Underscript m equals 0 Overscript up er M Subscript s Baseline minus 1 Endscripts times c Subscript s Baseline Subscript Baseline left-parenthesi m right-parenthesi times n Subscript Baseline Subscript s Baseline times left-parenthesi m minus k right-parenthesi period

(13) The outputs of the matched filter are averaged over NSy symbols to reduce the influence of the noise. ModifyingAbove x With bar left-parenthesi k right-parenthesi equals normal up er Sigma Underscript n equals 0 Overscript up er N Subscript up er S y Baseline minus 1 Endscripts x times left-parenthesi k plus n up er M Subscript up er S Baseline right-parenthesi period

(14) As shown in Figure 2, the output of the matched filter is determined by the auto-correlation function, us(k), of the spreading sequence, cs(k), and the impulse response, hl. Suppose us(k) is the matrix whose elements are given by the autocorrelation function, us(k), = us(k)

[us(k),us(k — 1),....,

—(L — 1))]T.(15) us(k

The auto-correlation matrix of the spreading sequence is normalup erUSubscriptsBaselineSubscriptBaseline quals eft-bracketnormaluSubscriptsBaselineSubscriptBaselinetimesleft-parenthesi 0right-parenthesi com anormaluSubscriptsBaselineSubscriptBaselinel ft-parenthesi 1right-parenthesi com aelips com anormaluSubscriptsBaselineSubscriptBaselinetimesleft-parenthesi up erLminus1right-parenthesi right-bracketSuperscriptup erTBaseline qualsStar 4By3Matrix1stRow1stColumnuSubscriptsBaselinel ft-parenthesi 0right-parenthesi 2ndColumn elips 3rdColumnuSubscriptsBaselinel ft-parenthesi minusleft-parenthesi up erLminus1right-parenthesi right-parenthesi 2ndRow1stColumnuSubscriptsBaselinel ft-parenthesi 1right-parenthesi 2ndColumn elips 3rdColumnuSubscriptsBaselinel ft-parenthesi minusleft-parenthesi up erLminus2right-parenthesi right-parenthesi 3rdRow1stColumn elips 2ndColumn elips 3rdColumn elips 4thRow1stColumnuSubscriptsBaselinel ft-parenthesi up erLminus1right-parenthesi 2ndColumn elips 3rdColumnuSubscriptsBaselinel ft-parenthesi 0right-parenthesi EndMatrixperiod

(16)

Here, for simplicity, the noise is neglected. The output of the matched filter is left-bracket imesStarLayout1stRow ModifyngAbovexWithbarleft-parenthesi 0right-parenthesi 2ndRow ModifyngAbovexWithbarleft-parenthesi 1right-parenthesi 3rdRow elips 4thRow xoverba left-parenthesi up erLminus1right-parenthesi EndLayoutright-bracket qualsStar 4By3Matrix1stRow1stColumnuS bscriptsBaselinel ft-parenthesi 0right-parenthesi 2ndColumn elips 3rdColumnuS bscriptsBaselinel ft-parenthesi minusleft-parenthesi up erLminus1right-parenthesi rght-parenthesi 2ndRow1stColumnuS bscriptsBaselinel ft-parenthesi 1right-parenthesi 2ndColumn elips 3rdColumnuS bscriptsBaselinel ft-parenthesi minusleft-parenthesi up erLminus2right-parenthesi rght-parenthesi 3rdRow1stColumn elips 2ndColumn elips 3rdColumn elips 4thRow1stColumnuS bscriptsBaselinel ft-parenthesi up erLminus1right-parenthesi 2ndColumn elips 3rdColumnuS bscriptsBaselinel ft-parenthesi 0right-parenthesi EndMatrixStar 4By1Matrix1stRow h02ndRow h13rdRow elips 4thRow hSubscriptup erLminus1BaselineEndMatrixperiod

(17)

Hence,

normal upper X overbar equals normal upper U Subscript s Baseline dot Subscript Baseline normal h comma

(18) where

normal up er X overbar equals left-bracket ModifyingAbove x With bar left-parenthesis 0 right-parenthesis comma ModifyingAbove x With bar left-parenthesis 1 right-parenthesis comma el ipsis comma x overbar left-parenthesis up er L minus 1 right-parenthesis right-bracket Superscript up er T Baseline period

(19) Therefore, the impulse response, h, can be estimated with the output of the matched filter, X , and the inverse of the auto-correlation matrix, Us—1, as follows. normal h equals normal upper U Subscript s Superscript negative 1 Baseline times dot normal upper X overbar

(20) 2.2. Pseudo-Inverse with a Threshold If the baseband filter is used for pulse shaping, the chip waveform is no longer the rectangular shape and the waveform of the spreading sequence becomes smooth. The impulse response of the channel is estimated by using this filtered spreading sequence. The impulse response of the channel is estimated as normal h equals upper U Subscript s Superscript prime negative 1 Baseline dot times normal upper X overbar prime period

(21) from Eqs. (16)— (19) where X is the output of the matched filter and is the auto-correlation matrix of the filtered spreading sequence. However, h cannot be estimated precisely with the filtered spreading sequence due to the waveform of the spreading sequence. When the differences between the samples in cs(k) are small, the columns of er are not independent and the rank of the matrix, lk reduces. Hence, the inverse matrix of we cannot be derived precisely. In order to improve the accuracy, the channel estimation with a pseudo-inverse is employed [7 ]. matrix, YU instead of the inverse matrix, df Singular value decomposition is applied to ui ,

,

,

normal up er U Subscript Baseline prime Subscript s Baseline equals normal up er W normal up er Sigma times normal up er V Superscript up er T

(22)

where W and V are matrices that have of ty are [σ1,....,σq]. Hence,

Σ where q is the rank of

pseudo-inverse matrix,

df

gh

=

diag(σ1,σ2,.σq,, Singular

.

orthogonal columns and the singular values 0,....,0)(23) value

decomposition

values of

to the

(24) =

singular

applied

,

fg

and the

is also

U^"

are

W+Σ+VT

[1/eri.l/rr;y|.

Hence,

normal up er Sigma Superscript plus Baseline equals d i a g left-parenthesis StartFraction 1 Over sigma 1 EndFraction comma StartFraction 1 Over sigma 2 EndFraction comma el ipsis comma StartFraction 1 Over sigma Subscript q Baseline EndFraction comma 0 comma separator comma 0 right-parenthesis times period

(25) From Eqs. (23) and (25) when the singular value, σq,in U's is small, a small difference in σ results in large fluctuation to its reciprocal, 1/σ. Hence, the pseudo,

inverse matrix, U's+, cannot be derived precisely. In the proposed scheme, a threshold is set for deriving the pseudo-inverse matrix. If the singular value is smaller than the

threshold, the singular value is

set to 0.

3. Measurement Results 3.1. Experiment Setup 3.1.1. Reference Impulse Response Measurement with a Vector Network Analyzer The measurement is conducted to investigate the impulse response of the channel in a room whose size is 5.2 [m] × 6.7[m] × 3.4 [m].

Figure 3. Measurement room

Table 1. 1. Measurement Measurement equipments Table Version

Equipment Vector Network Analyzer (VNA) USB/GPIB Interface VNA Software Tx Antenna (height: 10cm) Rx Antenna (height: 10cm)

Agilent 8753ET Agilent 82357A Agilent technology Intuilink ( version 1.3) Monopole antenna Collinear array antenna

Table 2. 2. Measurement Measurement conditions conditions Table

Frequency range Measurement points Sweep time Measurement step Fs

from 2.2

[GFlz]

to 2.64

[GFlz] 801

0,3[s] 0.55[MHz]

The impulse response of the channel is measured in both line-of-sight (LOS) and non-LOS (NLOS) situations. In order to realize the NLOS condition, the Tx antenna is placed at the outside of the room. The equipments used for the measurement are shown in Table 1. Table 2 shows the measurement conditions of the vector network analyzer (VNA). The impulse response of the channel is obtained with the measured S21 parameters. The chip rate of the spreading sequence of the IEEE802.11b receiver is 11 [Mcps]. When the RAKE receiver with fractional sampling is employed, the sampling frequency is 44 [MHz]. Therefore, the resolution of the delay is 0.189 [ns] that is equal to the inverse of 44 [MHz]. 3.1.2. Impulse Response Estimation with an IEEE802.11b WLAN card Figure 4 shows the experiment setup with a WLAN card (corega, CGWLCB54GTU2). The WLAN card is set as an access point and beacon signal is used as a transmitted signal that is continuously generated. The beacon interval is set to be 1 [ms] [8]–[10]. The transmitted signal is received via the receiving antenna and downconverted to the baseband signal. The baseband signal is digitized by the A/D boards at the rate of 1[GHz]. The detection period of the received signal is 1/4 [s]. The samples are decimated to achieve the sampling speed of 44 [MHz]. Finally, the impulse response of the channel is estimated by the proposed scheme.

Figure 4. Experiment system

Figure 5. Normalized impulse response (LOS)

3.2. Measurement Results 3.2.1. Measurement with the VNA The impulse response in the LOS situation and the NLOS situation are shown in Figures 5 and 6. Figure 5 shows that the direct path is strong in the case of the LOS condition and Figure 6 shows that multiple weak paths can be found in the case of the NLOS condition. The path is considered to exist if the normalized impulse response is

Figure 6. Normalized impulse response (NLOS)

Figure 7. MSE vs. Threshold (LOS), Threshold = 0.2

~40

larger than 0.1. These responses are used as the reference in order to calculate the MSE performances of the proposed scheme. Here, a window size is employed to derive the MSE correctly. In this measurement, the window size is set to 5 [Tc/4] in Figures 5 and 6. This is because the major paths exist within the delay of 5 [Tc/4]. 3.2.2. Estimation with the IEEE802.11b WLAN card The relation between the threshold of the singular value and the MSE are shown in Figures 7 and 8.

Figure 8. MSE vs. Threshold (NLOS), Threshold = 0.2 ~ 70

Figure 7 shows that the minimum MSE is gained when the threshold is in the range of about 5.5 to 20 in the case of the LOS condition. On the other hand, in the case of the NLOS condition, the minimum MSE can be found when the threshold is in the range of about 30 to 60 as shown in Figure 8. Next, the minimum value of the MSE in the

case of the LOS condition is with that of the NLOS condition. 7 compared Figures and 8 show that the minimum MSE for the LOS situation is about 0.012 and for the NLOS situation is about 0.17. Therefore, the accuracy of channel estimation in the case of the LOS condition is better than that in the case of the NLOS condition. This is because one strong path can be observed in the LOS situation while multiple weaker paths can be observed in the NLOS situation.

4. Conclusions In this chapter, a channel estimation scheme for the IEEE802.11b WLAN system is investigated through the experiment. In the conventional scheme, the impulse response of the multipath channel is estimated with a pseudo-inverse matrix. However, this scheme is not robust to noise. Therefore, the pseudo-inverse matrix with a threshold is proposed. It is concluded that the channel can be estimated precisely with the optimum threshold and that the accuracy of channel estimation in the case of the LOS situation is better than that of the NLOS situation.

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Hong and K. C. Whang Effect of tap spacing on the performance of direct-sequence spread-spectrum RAKE receiver ", IEEE Transactions on Communication vol. 48 K. J. Kim S. Y Kwon E. K. ,

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Hybrid-ARQ Techniques and its Application in 4G Wireless Systems Dheeraj Sreedhara,1 a Sasken Communication Technologies., Bangalore, India. Abstract. Hybrid-Automatic Repeat-reQuest (H-ARQ) methods have been gaining lot of popularity with the recent wireless standards. H-ARQ is a modification of conventional ARQ techniques implemented by the link/transport layer, wherein the receiver requests for a re-transmission of an in-correctly received packet or alternatively, the transmitter keeps transmitting a packet until an acknowledgement for the same is received. In H-ARQ, the forward-error correction (FEC) techniques implemented at the physical layer is used in conjunction with the packet re-transmissions and hence H-ARQ performs better than conventional ARQ in poor signal conditions but at the cost of reduced throughput in strong signal conditions. H-ARQ has been extensively studied in research literature and several variants have been proposed and analyzed. Another, recent development has been the use of multiple input multiple output (MIMO) techniques along with H-ARQ. It has been shown that, when a receiver feed back for a transmitted packet is available at the transmitter, for a given spatial multiplexing gain of a MIMO channel, the reliability of the channel, measured in terms of maximum achievable diversity, is enhanced. This chapter covers in detail the study and analysis of the recent developments in H-ARQ as well as MIMO H-ARQ. Uses and application of H-ARQ and MIMO H-ARQ in IEEE 802.16e have also been covered. Keywords: Wireless Telecommunications, 4G standards. ARQ, H-ARQ, MIMO H-ARQ.

1. Introduction errors is mandatory for any wireless communication syscategories of techniques for handling errors. i) Addition of redundant information in the data which is capable of correcting errors within some bound

Handling

of transmission

tem. There are two

(Forward error correction, FEC) and ii) Error detection combined with request for popularly called as Automatic repeat-request (ARQ).

retransmission which is

FEC utilizes error-correcting codes to handle transmission errors. These codes have limited error-correcting capabilities and, if the decoder is unable to correct the transmission errors, the incorrect data buffer is delivered to the higher layers. In this case, the data throughput is maintained at a fixed level, which is equal to the code rate of the FEC. The “goodput” which is measured in terms of the rate of correctly delivered packets might be lesser than the throughput. Another drawback with the FEC scheme is that, in order to maintain a high level of reliability in poor

1 Corresponding Author: Dheeraj Sreedhar, Sasken Communication Technologies, 139/25, Ring Road, Domlur Bangalore 560 071, India. Email: [email protected].

DOI: 10.1201/9781003336853-20

Hybrid-ARQ Techniques and its Application in 4G Wireless Systems

received signal power levels, long and powerful code has to be used which results in a significant wastage of bandwidth in good signal conditions. ARQ schemes, on the other hand, use an error detection code to detect the presence of errors. If an error is detected in a particular packet, the receiver requests for a re-transmission of the same packet. The erroneous packet is typically discarded. This process goes on until the receiver does not detect an error in the packet, or if the number of re-transmissions has reached a threshold, depending on the implementation. Since the error detection code can also, not detect an error, which may be present, there is a non-zero probability that an in-correct data packet is delivered to the higher layers. However, since the probability of a decoding error in the case of FEC is much higher than the probability of un-detected error in the case error detecting codes in ARQ, the reliability is much higher in the case of ARQ. The main drawback of ARQ is that the throughput decreases rapidly as the signal conditions deteriorates. The strengths and weakness of ARQ and FEC can be complemented if they are combined in an appropriate manner. When FEC techniques are used in conjunction with ARQ, it is called Hybrid-ARQ (H-ARQ). An FI-ARQ system essentially embeds an FEC system inside an ARQ system. The role of FEC is to minimize the number of re-transmissions in an ARQ system thereby increasing its throughput. H-ARQ has been extensively studied in the literature and most of the schemes can be broadly classified into two, Type-I and Type-II, which would be elaborated later in this chapter. A key metric to measure the effectiveness of H-ARQ schemes is throughput. We will derive closed form analytical expressions for the various H-ARQ schemes. Another aspect of H-ARQ system that is of importance is the total transmission delay. Real-time multimedia communications impose restrictions on the maximum delay that can be incurred.

Multiple Input Multiple Output (MIMO) techniques add another dimension to H-ARQ. In conventional H-ARQ, the re-transmissions happen at another time instant and hence, the re-transmitted packet experiences a different channel thereby exploiting the temporal diversity of the channel. With multiple transmit and receive antennas, the re-transmission can happen over another spatial channel thereby exploiting the spatial diversity of the channel. There are two gains from a MIMO system, i) spatial multiplexing gain which quantifies the increase in possible data rate due to the multiple spatial paths available and ii) diversity gain which quantifies the increase in reliability of the channel and it is known that there is a fundamental trade-off between the two. But, it has been proven in [10] that with ARQ, for a given spatial-multiplexing gain, the achievable diversity gain could be enhanced. This chapter will discuss some of the MIMO-H-ARQ transmission schemes. This chapter is organized as follows. Sec. 2 contains the description and analysis of the conventional ARQ schemes. Different protocols for re-transmission and feedback are discussed. Sec. 3 describes Type-I and Type-II H-ARQ schemes and analyses the performance gains. Sec. 3 also contains different code-combining strategies that can be employed with H-ARQ. In Sec. 4, the basic gains in terms for diversity multiplexing gain advantage for a MIMO-H-ARQ system are described first followed by a discussion on some of the MIMO-H-ARQ schemes proposed in the

2. Conventional ARQ

literature as well as various receiver architectures for the same. The application of H-ARQ techniques in recent WiMax standard is given in Sec. 5.

2. Conventional ARQ Conventional ARQ is based on error detection and a retransmission protocol. The effectiveness of the ARQ techniques is based on i) effective error detection codes which has a very low probability of not detecting an error at the same time having minimal overhead and ii) effective of the re-transmission protocol which incurs less transmission overheads and delays. Error detection is typically done through a CRC or a checksum. The transmitted packet formation is illustrated in Figure 1. Once the error is detected, it has to be communicated to the transmitter and the re-transmission policy decides how this communication is done and how the transmitter does the re-transmission. There are broadly three classes of re-transmission

polices. i) stop-and-wait (SAW), ii) selective-repeat (SR) iii) go-back-n (GBN). In SAW, as the name suggests, the transmitter waits for a reply from the receiver. There can be 3 possible outcomes. i) The receiver responds with an acknowledgement (ACK) message suggesting that the receiver did not detect any error in the transmitted packet ii) The receiver gives a negative acknowledgement (NACK) suggesting that the receiver detected an error in the packet and iii) There is no response from the receiver suggesting that the packet was not detected at all. In the second case, the transmitter re-transmits the packet on receiving the NACK whereas in the third case the transmitter re-transmits the packet after waiting for a pre-defined time for a response from the receiver. This cycle could go on forever, but typical implementations will have a retransmission limit beyond which there will not be any re-transmission. The transmit-receive sequence for the SAW protocol is illustrated in Figure 2. While the key strength of this algorithm is its simplicity, it is obvious that, the transmitter spends considerable time waiting and this, results in larger delays. One way to circumvent this is by using multiple channels for transmitreceive pairs. In SR protocol, the transmitter continuously transmits packets and the receiver NACK's only those packets on which it detects errors. Hence the receiver sends a re-transmission request only for the erroneous packets. Though the transmission efficiency is greatly improved in this case, the main draw back is that the receiver has to buffer the packets received in out of order sequence. The transmit-receive sequence for the SR protocol is illustrated in Figure 3.

Figure 1. Transmitted packet formation for conventional ARQ

Figure 2. Transmit-receive sequence for stop-and-wait protocol

Figure 3. Transmit-receive sequence for selective-repeat protocol

GBN protocol is a slight improvisation over SR protocol in the sense that receiver requests for a re-transmission from the point from which it first detects an error. Though there is a loss in transmission efficiency, the receiver buffering complexity is reduced in this case. 2.1. Throughput and Reliability Analysis The throughput of an ARQ system is measured in terms of the average number of data packets accepted by the receiver in the time that it takes the transmitter to send single data packet. Let K be the length of the data packet and let N be the length of the transmitted packet, N − K being the number of error detection parity bits added. Then the throughput is given by eta times equals times left-parenthesi StartFraction up er K Over up er N EndFraction right-parenthesi times left-parenthesi StartFraction 1 Over up er T overbar Subscript r Baseline EndFraction right-parenthesi times com a

where T is the expected number of re-transmissions before a packet is accepted. If T is the maximum number of re-transmissions allowed and p is the probability of failure in the i’th retransmission, then T can be written as up erToverbarSubscriptrBaseline qualsnormalup erSigmaUnderscriptkequals1Overscriptup erTSubscriptrSuperscriptmaxBaselineSubscriptBaselineEndscriptskleft-parenthesi 1minuspSubscriptBaselineSubscriptrSuperscriptleft-parenthesi kright-parenthesi BaselineSuperscriptBaselineright-parenthesi tmesnormalup erPiUnderscriptjequals1Overscriptkminus1Endscripts imespSubscriptrSuperscriptleft-parenthesi jright-parenthesi BaselineSuperscript

Assuming that p

is independent of i, this can be simplified as,

up erToverbarSubscriptrBaselinetimesequalstimesStartFraction1hyphenleft-parenthesi up erTSubscriptrSuperscriptmaxBaselineSuperscriptBaselineplustimes1right-parenthesi timesleft-parenthesi pSubscriptrBaselineright-parenthesi Superscriptup erTSuperSubscriptrSuperSuperscriptmaxSuperscriptSuperSuperscriptSuperscriptBaselinetimesplusup erTSubscriptrSuperscriptmaxBaselineSuperscriptBaselinetimesleft-parenthesi pSubscriptrBaselineright-parenthesi Superscriptleft-parenthesi up erTSuperSubscriptrSuperSuperscriptmaxSuperscriptSuperSuperscriptSuperscript lustimes1right-parenthesi BaselineOver1minuspSubscriptrBaselineEndFraction

Assuming that any number of re-transmissions are allowed, i.e., T this simplifies to

→∞,

up er T overbar Subscript r Baseline times equals times StartFraction 1 Over 1 minus p Subscript r Baseline EndFraction

The reliability is measured in terms of the rate at which an incorrect packet is accepted. Let p denote the probability of not detecting an error at the i’th transmission, then the residual packet error rate is given by, pertimesequalsnormalup erSigmaUnderscriptkequals1Overscriptup erTSubscriptrSuperscriptmaxBaselineEndscripts imespSubscriptdSuperscriptleft-parenthesi kright-parenthesi Baselinetimesnormalup erPiUnderscriptjequals1Overscriptkminus1Endscripts imespSuperscriptBaselineSubscriptrSuperscriptleft-parenthesi jright-parenthesi

Again assuming that p

and p

is independent of i, this can be simplified as,

p e r times equals times StartFraction p Subscript d Baseline times plus times left-parenthesi 1 times hyphen p Subscript r Baseline minus p Subscript d Baseline right-parenthesi times left-parenthesi p Subscript r Baseline right-parenthesi Superscript up er T Super Subscript r Super Superscript max Superscript Super Superscript Superscript Baseline Over 1 minus p Subscript r Baseline EndFraction

and under infinite number of re-transmissions ( T

→∞), this simplifies to

p e r times equals times StartFraction p Subscript d Baseline Over 1 minus p Subscript r Baseline EndFraction

A detailed analysis of the delay can be found in [5].

3. H-ARQ H-ARQ schemes can broadly be classified into two, i) Type-I and ii) Type-II. 3.1. Type-I H-ARQ Type-I H-ARQ is the simplest extension

over conventional ARQ where the data after the addition of error detection packet parity bits is further encoded by a forward error correcting code, which adds error correcting parity bits. At the receiver, the error correction parity bits are used to correct transmission errors and the error corrected output is then tested by the error detection code to determine if the packet is indeed error free. If the error detection tests positive, retransmission of the packet is requested just as in the case of conventional ARQ. If the signal conditions are poor, then there is a lesser probability of re-transmission request compared to conventional ARQ and hence higher throughput. However, if the signal conditions are good, then the added error-correction bits just reduces the throughput. Hence, there

Figure 4. Packet formation for Type-I H-ARQ

is a crossover point in signal strength above which conventional ARQ performs better than Type-I H-ARQ in terms of throughput [4]. In terms of reliability, Type-I H-ARQ clearly outperforms conventional ARQ. Type-I H-ARQ can be combined with any of the tree transmission protocols SAW, GBN or SR. The throughput and reliability analysis done for the conventional ARQ applies for the case of Type-I, with the difference that in the case of Type-I H-ARQ, N includes error-correcting parity bits in addition to the error-detecting bits and the probability of error, pr, is with the error detection code. Ideally, the number of error correction bits added should be a function of the signal condition where more number of error protection is added in bad signal conditions and vice-versa. This can be achieved by the concept of puncturing through convolutional codes. A mother rate 1/N convolutional code is repeatedly punctured with a specified period to obtain a family of lower rate codes. The rate of puncturing can be altered based on signal strength levels. Figure 4 illustrates the packet formation for Type-I H-ARQ. 3.1.1. Chase Combining In Type-I H-ARQ, at subsequent re-transmissions, the receiver receives different noisy versions of the same FEC encoded data in packet. In [1], the author proposed a code-combining algorithm for combining and decoding an arbitrary number of noisy packets. This algorithm is popularly known chase combining. 3.2. Type-II H-ARQ Type-II H-ARQ, first proposed in [2], consists of transmitting the error-correcting parity bits only when the first data transmission fails. Here the first transmission is identical to that of conventional ARQ. Also, the error correcting code is invertible, i.e., it is possible to reconstruct the data packet from the error-correcting parity bits as well. A rate 1/N code outputs N packets that could be decoded independently. The number of output packets could be reduced or controlled by puncturing [7].

Figure 5. Packet formation for Type-II H-ARQ

Figure 6. Transmit-receive sequence for Type-II H-ARQ with SAW protocol In the first

the

error

error

transmission, the packet, P which contains the data packet along with parity bits is send, if this is not successfully received, then the

detection

correcting parity

bits for the

same

data

along with the error detection bits for

these parity bits, p is send in the second transmission. After the N'th transmission, the first packet is repeated. It is possible to decode each of them independently and it is also possible combine these packets to obtain a better estimate. Hence, Type-II H-ARQ works with the efficiency of conventional ARQ in good signal conditions and to large extent to that of Type-I H-ARQ in bad signal conditions. In [3 ], the authors proposed a small modification over Type-II H-ARQ in which the error detection parity bits are not calculated and added for every re-transmission block, but is calculated and added before being input to the FEC itself. Figure 5 illustrates the packet formation for a generalized Type-II H-ARQ.

As in Type-I H-ARQ, Type-II H-ARQ can also be combined with any of the transmission protocols SAW, GBN or SR. Figure 6 shows the transmit-receive sequence of Type-II H-ARQ with SAW protocol. In Type-II H-ARQ, the packet error probability p is not independent of i. A detailed analysis of throughput, reliability and delay for Type-II H-ARQ can be

found in [6 ], [8 ]. It is also possible to use a more powerful code like Turbo or LDPC and get much better performance. Various algorithms for combining the different noisy packets have been proposed. A selective combining algorithm, which performs better in non-stationary bursty channel, has been proposed in [9 ].

4. MIMO H-ARQ With multiple transmit and receive antennas there is another dimension, in which data can be transmitted, viz. space. Just as in Type-II H-ARQ, the error-detection parity bits are transmitted on request, in the MIMO scenario, the redundant transmission (space-time coded) on the multiple transmit antennas can be transmitted only when the earlier transmission has failed. 4.1. Diversity-Multiplexing Tradeoff for

the MIMO-ARQ Channel

A MIMO system has two types of gains. i) The data streams can be transmitted in parallel across different transmit antennas, there by increasing the transmission rate. This is called spatial-multiplexing gain. ii) The same data could be coded and transmitted from a different transmit antenna thereby increasing the reliability of the transmission. This is called diversity gain. It is known [10] that there is a fundamental tradeoff between the two and the maximum achievable diversity gain for a given spatial-multiplexing gain is bounded. This trade-off is called the diversitymultiplexing gain (D-MG) tradeoff. For a MIMO system with Nt transmit and Nr receive antennas, the maximum achievable spatial multiplexing gain is min{Nt, Nr}. For any spatial multiplexing gain, k, between 0 and min{Nt, Nr}, the maximum achievable diversity advantage is given by the piece-wise linear function f(k) connecting the points (k, (Nt − k)(Nr − k)). In [11] the authors have shown that given a fixed number of ARQ rounds R, the achievable diversity order for a spatial multiplexing gain of k is given by f(k/R). The increase in diversity order is illustrated in Figure 7.

Figure 7. D-MG trade-off curves for MIMO-H-ARQ channel with different no. of ARQ rounds R

MIMO-ARQ is illustrated using a simple two-transmit antenna case using the Alamouti [ 13] space-time code. In the first time instant, transmit antenna 1 transmits X1 and antenna 2 transmits X2 (X1 and X2 are modulated symbols for packet P1 and P2 respectively which contains error detection parity bits as well). If there are more than 2 receive antennas and the channel paths are not correlated, it is possible to decode this information. If the decoder detects an error in this transmission, then it requests for a re-transmission and the transmitter sends x on transmit antenna 1 and A on antenna 2. The decoder can combine this transmission with the earlier transmission and obtain a diversity order of 2 for the second detection. Hence it is obvious that for the MIMO-ARQ channel can achieve a better D-MG tradeoff than the pure MIMO channel. —

4.2. Generalized MIMO-ARQ Transmission and Receiver Design Figure 8 illustrates a generalized MIMO transmission and receptions with Nt transmit antennas, Nr receive antennas and K rounds of ARQ. Let X(k) denote the transmitted vector at the k’th ss =

,

round of ARQ. It is noted that x 1, Nt, are space-time encoded modulated symbols corresponding to either one coded data packet in which case it is called “vertical encoding or Nt independent data packets in which case it is called horizontal encoding. It is assumed that the data packets contain error detecting par-

ity bits

as

well. Let Y(k)

vector. Let H

=

Y

i

=

...,

denote the

corresponding received

denote the channel fade from the i’th transmit antenna to the j'th

receive antenna at the k'th round of ARQ and let H denote the Nt x Nr matrix the channel fades at the k'th round of Then Y(k) can be written as ARQ. containing up er Y Superscript left-parenthesi k right-parenthesi Baseline times equals times up er H overbar Superscript left-parenthesi k right-parenthesi Baseline times up er X Superscript left-parenthesi k right-parenthesi Baseline times plus up er N Superscript left-parenthesi k right-parenthesi

Figure 8. Generalized MIMO-ARQ transmission and reception

For the first detection (of X(1)) detection schemes similar to V-BLAST [14] or lattice reduction [15] can be used. For the subsequent ARQ detections various combining schemes have been proposed [12], [19].

5. H-ARQ in IEEE in 802.16e (WiMax) H-ARQ techniques have been adopted in all the 4G wireless standards, IEEE 802.16e, UMB and LTE [16]–[18]. This section will cover the implementation of H-ARQ in 802.16e standard (WiMax) [16]. In the WiMax standard, there is provision for conventional ARQ at the MAC layer level. ARQ is implemented through SR transmission protocol and a compact bitmap based feedback is used. In order to reduce the feedback overhead, the ACK/NACK feedbacks could be sent either as a stand-alone management messages or along with the other payload data. For H-ARQ, there is provision for either Type-I or Type-II H-ARQ schemes. H-ARQ could be implemented either with a convolutional code (CC) or a convolutional turbo code (CTC). Unlike ARQ at the MAC layer, H-ARQ is implemented using the SAW transmission protocol but there is provision for multi-channel H-ARQ. For MIMO-H-ARQ, the following transmission schemes are used in IEEE IEEE 802.16e Table 1. 1. Illustrating the various various MIMO-H-ARQ schemes schemes used used in 802.16e Illustrating the Table Nt

First Transmission

Even Transmission

2

[xum

pst.tfaj

3

[Zi,X2,X3]

4

[XuX2,Xi,X4]

Odd Transmission

[XUX2,X3]

[~X*V X*.-X*4, X*\

[XuX2,Xi,X4]

References [1]

“

D. Chase

combining a maximum likelihood decoding approach for combining an arbitrary packets," IEEE Transactions on Communications vol. 33 pp. 385 393 May 1985 S. Lin and S. Y. Philip A hybrid ARQ scheme with parity retransmission for error control of satellite channels ,” IEEE Transactions on Communications vol. 30 no. 1 July 1982 Y.-M. Wang and S. Lin Amodified selective-repeat type-II hybrid ARQ system and its performance analysis ,” IEEE Transactions on Communications vol. 31 no. 5 pp. 593 608 May 1983 R. Comroe and D. J. Costello Jr ARQ schemes for data transmission in mobile radio systems,” IEEE Transactions on Vehicular Technology vol. 33 no. 2 pp. 88 97 July 1984 D. Towsley and J. Wolf On the statistical analysis of queue lengths and waiting times for statistical multiplexers with ARQ retransmission schemes," vol. 27 no. 4 pp. 693 702 IEEE Transactions on Communications April 1979 S. Kallel Analysis of a type II hybrid ARQ scheme with code combining,” vol. 38 no. 9 pp. 1133 1137 IEEE Transactions on Communications August 1990 ,

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S. Kallel and D. Haccoun Generalized type II hybrid ARQ scheme using punctured convolutional coding,” vol. 38 no. 11 pp. 1938 1946 IEEE Transactions on Communications November 1990 [8] Q. Yang and V. K. Bhargava Delay and coding gain analysis of a truncated type-II hybrid ARQ protocol ,” vol. 42 no. 1 pp. 22 32 IEEE Transactions on Vehicular Technology February 1993 [9] Q. Zhang and S. A. Kassam Hybrid ARQ with selective combining for fading channels ,” vol. 17 no. 5 IEEE Journal on Selected Areas in Communications May 1999 [10] L. Zheng and D. Tse Diversity and multiplexing: A fundamental tradeoff in multiple-antenna channels,” IEEE Transactions on Information Theory , vol. 49 no. 5 pp. 1073 1096 May 2003

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H. El Gamal G. Caire and M. O. Damen

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The MIMO ARQ channel:

Diversity-multiplexing-delay tradeoff,” vol. 52 no. 8 pp. 3601 3621 IEEE Transactions on Information Theory August 2006 [12] E. N. Onggosanusi A. G. Dabak Y. Hui and G. Jeong Hybrid ARQ transmission and combining for MIMO systems communications ,” vol. 5 pp. 3205 3209 ICC May 2003 [13] S. M. Alamouti A simple transmit diversity technique for wireless communications ,” IEEE Journal ,

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Selected Areas in Communications vol. 16 pp. 1451 1458 October 1998 G. D. Golden G. J. Foschini R. A. Valenzuela and P W. Wolniansky Detection

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laboratory results using V-BLAST,” Electronic Letters

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Lattice-reduction-aided detectors for MIMO communication systems ,” Proceedings ofIEEE Globecom pp. 424 428 Taipei, Taiwan November 2002 IEEE std 802.16e. Part 16: Amendment 2: Physical and Medium Access Control Layers for Combined Fixed and Mobile Operation in Licensed Bands 2005 3GPP2 C.S0084-001-0 v1.0, Physical Layer for Ultra Mobile Broadband 11 Mil) Air Interface Specification, Version 1.0 April 5 2007 .” 3GPP TR 25.814V7.1.0, Physical Layer Aspects for Evolved Universal Terrestrial Radio Access " 3GPP TSG-RAN1, Update on MIMO and HARQ Interactions ,” Denver, USA 13 17 February H. Yao and G. W.Wornell

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2006

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C\ Taylor & Francis ~

Taylor&FrancisGroup http://taylo ra ndfra n ci s.com

Multiuser Diversity in MIMO Systems: Theory and Performance Xing ZHANGa,1, Wenbo WANGa a Wireless Signal Processing and Networks (WSPN), Key Lab of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing, China Abstract. This paper presents a comprehensive framework to analyze the performance of multiuser diversity (MUD) in multiple-input multiple-output (MIMO) systems. Based on this framework, the tight closed-form expressions of outage probability, outage capacity and average symbol error rate of multiuser diversity are derived for the MIMO transmit antenna selection with maximal-ratio combining (TAS/MRC) system, by which we show how and with what characteristics antenna selection gains, MIMO antenna configurations and fading gains impact on the system performance, with an emphasis on the study of multiuser diversity (MUD) influence. From both theoretical and simulation results, our study shows that in MIMO TAS/MRC systems the number of users plays a key role in the system performance and can be viewed as equivalent “virtual” transmit antennas, which is the source of the inherent multiuser diversity gain.

Keywords: MIMO multiuser diversity (MUD), outage probability, outage capacity, symbol error rate.

1. Introduction During recent years, there have been many attempts in finding techniques to achieve high quality and high data rate transmissions over mobile radio channels, for example, China’s national basic research program (973 program) has recently launched a project about multi-domain cooperative broadband wireless network [1] to extract possible performance gains in various resource domains. From the physical layer’s perspective, wireless communications using multiple transmit and receive antennas, known as multiple-input multiple-output (MIMO) systems [2], offers key advantages over single-input single-output (SISO) systems, such as antenna diversity and spatial multiplexing gains. In point-to-multipoint (PMP) communication links, that is, in a multiuser system one base station (BS) communicates with K users, the propagation channels between BS and users are independent for each user and thus the channel that is in a deep fade for one user may be good for another. Thus the overall system throughput is maximized by allocating channels to one of the K users who can achieve the largest throughput on it [3]. This performance gain is inherent in multiuser system and is called the multiuser diversity (MUD) (which is first motivated 1 Xing Zhang: P.O.Box 93, Beijing University of Posts and Telecommunications (BUPT), Beijing 100876, China. (email: [email protected])

DOI: 10.1201/9781003336853-21

Multiuser Diversity in MIMO Systems: Theory and Performance

by an information-theoretic result in [3]). This kind of diversity can be explained as an analogy of the water-filling principle across multiple users — “pouring” more resources to the user with better channel quality [8]. In point-to-point (P2P) communication links, multiple antennas have been widely used to achieve antenna diversity [4] as a mean to mitigate signal-level fluctuations by fading. Furthermore, many schemes jointly use transmit and receive antenna diversity techniques at both ends, e.g., MIMO transmit antenna selection with maximal-ratio combining (TAS/MRC) [5] is one of the diversity scheme which has received considerable studies. The idea of MIMO TAS/MRC can be briefly described as follows: by using channel state information (CSI) feedback, the best transmit antennas out of all Nt transmit candidates, which maximizes the postprocessing SNR at the MRC output of Nr receive antennas, is selected to transmit data. The benefit of this diversity scheme is that only partial CSI feedback is needed instead of full CSI, which costs much less feedback bandwidth. Another advantage is that at the transmitter only one RF chain is needed since only one antenna is selected, which can significantly reduce the transmitter’s cost and complexity. The literature survey with the analysis of MIMO transmit antenna selection with maximal-ratio combining is discussed as follows. [6 ] presents the outage probability of TAS/MRC system in Rayleigh fading channels. In [ 5 ][ 6], the authors derived the average bit-error-rate (BER) expression of transmit antenna selection system in a flat Rayleigh channel. Moreover, based on the model in [ 5 ][ 6 ], in [ 7] the authors present the symbol error probability (SEP) analysis of several constellations for perfect CSI feedbacks. In [8 ] channel capacity is analyzed for selective transmission with maximal-ratio combining system in both Nakagami and correlated Rayleigh fading channels. In summary and to the best of our knowledge, we note that most of the previous works are concentrated on the point-to-point communication links (i.e., single user system), very few works have addressed the analysis of the impact of multiuser diversity, antenna configurations, antenna array gains, etc. on the system performance. From a system perspective, a comprehensive performance analysis of multiuser diversity in point-to-multipoint (PMP) system is very urgent and beneficial to the practical design of MIMO wireless systems. In this paper, instead of considering only the point-to-point communication links, we focus on the performance analysis of MIMO TAS/MRC system in point-tomultipoint (PMP) communication link, that is, we concentrate on the performance analysis of multiuser diversity from a whole system with multiusers’ perspective. First a framework is presented to analyze the three most important performance metrics, i.e., outage probability, outage capacity and average symbol error rate; then based on this framework we theoretically study how and with what characteristics antenna selection gains, MIMO antenna configurations, multiuser diversity and fading gains impact on the system performance. Specifically, the major contributions and conclusions of this paper

are

summarized

as

follows,

• A tight analytical closed-form outage probability formula and its approximation are derived, from which we show that the outage probability decreased by a factor of m (where m is the average SNR);

2. System Model for MIMO Multiuser Diversity •

A closed-form expression of the average outage capacity of MIMO system with K users is presented, which shows that 1) the outage capacity increases with the increase of mean of effective average SNR and decreases with the increase of variance of the effective SNR; and 2) the number of receive antennas should be no more than that of transmit antennas to obtain a

higher outage capacity. •

An exact closed-form symbol error rate (SER) expression and its approximated formula are obtained, from which we show that a diversity order KNt + 1) can be achieved, and what’s approximately equals to (KNtNr more, for very large number of receive antenna Nr, an diversity order equals to (KNtNr) can be extracted. From both theoretical and simulation results, our study shows that in MIMO TAS/MRC systems users can be viewed as equivalent “virtual" transmit antennas, which is the source of the inherent multiuser diversity (MUD). —

•

2. System Model for MIMO Multiuser Diversity Consider a typical downlink multiuser MIMO TAS/MRC system as shown in Figure 1. The channel between the transmitter and the kth user experiences a quasi-static and flat-fading Rayleigh channel, which is modeled as stationary and ergodic random process and is characterized by an Nr *Nt matrix such that m , whose elements are independent identical distribution (i.i.d.) complex Gaussian random variables with zero mean and unit variance.m denotes the channel coefficients between the ith transmit antenna and the jth receive antenna for the kth receiver. If the transmitter selects an arbitrary antenna i for data transmissions, at the kth receiver the Nr *1 received signal vector r(k) can be written as, normalrSuperscriptleft-parenthesi kright-parenthesi BaselinetimesequalstimesnormalhSubscriptiBaselineSubscriptSuperscriptleft-parenthesi kright-parenthesi BaselinesSuperscriptleft-parenthesi kright-parenthesi BaselinetimesplustimesnormalnSuperscriptleft-parenthesi kright-parenthesi

(1) where s(k) is the transmitted data symbol with average energy Es, n(k) represents the * 1 zero-mean additive white Gaussian which are modeled noise Nr (AWGN) vector, as i.i.d and having the single-sided power-spectral density of N0. The average SNR per data symbol (a.k.a. the input SNR or SNR at receive antenna) is m .

When maximal-ratio combining (MRC) is employed at the receiver, the postprocessing SNR at the MRC output when the ith antenna is selected for the kth user’ transmission can be written as, gam aSubscriptkSuperscipt Baselin SubscriptSupersciptBaselin times qualstimesStarFactionup erESubscriptsBaselin SubscriptBaselin Overup erN0EndFractionsigma-sum ationU dersciptjequals1Oversciptup erNSubscriptrBaselin EndscriptsStarAbsoluteValuehSubscriptjcom aiSubSupersciptSubscriptSupersciptleft-parenthesi kright-parenthesi Baselin EndAbsoluteValuesquared qualstimesgam aoverba sigma-sum ationU dersciptjequals1Oversciptup erNSubscriptrBaselin EndscriptsUndersciptOversciptEndscriptsStarAbsoluteValuehSubscriptjcom aiSupersciptleft-parenthesi kright-parenthesi Baselin EndAbsoluteValuesquared

(2) Similarly in [5][6], here m is distributed according to chi-square distribution with 2Nr degree of freedom [9], so its probability density function (PDF)

Figure 1. MIMO TAS/MRC system

is written as, fSubscriptkSuperscriptiBaselinetimesleft-parenthesi gam aright-parenthesi timesequalstimesStarFractiongam aSuperscriptup erNSuperSubscriptrSuperscriptminus1BaselineOverleft-parenthesi up erNSubscriptrBaselineminus1right-parenthesi timesfactorialgam aoverbarSuperscriptup erNSuperSubscriptrSuperscriptBaselineEndFractionexptimestimesleft-parenthesi minusStarFractiongam aOvergam aoverbarEndFractionright-parenthesi

(3) For multiuser diversity [3] with perfect feedbacks, the scheduler always allocates the radio resource to one user who can achieve the largest post-processing SNR when selecting the best transmit antenna, then the achieved effective post-processing SNR γs is

always the largest

one

in

i.e.,

m ,

gam a Subscript s Baseline times equals times gam a times left-bracket up er K up er N Subscript Baseline right-bracket equals max gam a Subscript k Superscript i Baseline k equals 1 com a 2 times elipsi up er K i tmes equals 1 com a 2 times elipsi up er N Subscript Baseline

(4)

According to order statistics [10], for i.i.d. random variables (RV), the PDF of the effective post-processing SNR γs in (4) is shown as follows, (let Z = K*Nt) fleft-parenthesi gam aright-parenthesi timesequalstimesStartFractionup erZOverleft-parenthesi up erNSubscriptrBaselinehyphen1right-parenthesi timesfactorialgam aoverbarEndFractionleft-bracket1hyphenexpleft-parenthesi minusStartFractiongam aOvergam aoverbarEndFractionright-parenthesi normalup erSigmaUnderscriptnequals0Overscriptup erNSubscriptrminus1BaselineEndscriptstimesStartFraction1OvernfactorialEndFractiontimesleft-parenthesi StartFractiongam aOvergam aoverbarEndFractionright-parenthesi SuperscriptnBaselineright-bracketSuperscriptup erZminus1BaselinetimesStartFractiongam aOvergam aoverbarEndFractionSuperscriptup erNSuperSubscriptrSuperscriptminus1Baselinetimesexpleft-parenthesi minusStartFractiongam aOvergam aoverbarEndFractionright-parenthesi

(5)

3. Performance Analysis of Multiuser Diversity In this section, based on the multiuser diversity model of MIMO TAS/MRC system proposed in Section 2, we present the theoretical performance analysis of the three most important performance metrics for multiuser diversity, i.e., outage probability, outage capacity and average symbol error rate in Subsection 3.1, 3.2 and 3.3, respectively.

3.1. Outage probability The spectral efficiency (channel capacity) under an effective SNR γs as in (4) of the MIMO TAS/MRC system (in bps/Hz) is written as, CTAS/MRC = log2(1 +γs)(6) Then outage probability is calculated as (here let m target value),

, C0 denotes the

m

(7)

After some manipulations, (7) can be written as (8). up erPSubscriptu perTup erAup erSslahup erMup erRup erCBaselin equalsStarFactionup erZOverl ft-parenthesi up erNSubscript Baselin minus1right-parenthesi factorialEndFractionsigma-sum ationU dersciptm inus0Oversciptu perZminus1EndscriptsUndersciptOversciptEndscriptsleft-parenthesi negative1right-parenthesi SupersciptmBaselin timesStarBinomialOrMatrixup erZminus1Cho semEndBinomialOrMatrixnormalup erSigmaUnderscipt minus0Oversciptmleft-parenthesi up erNSubscript minus1Baselin right-parenthesi EndscriptsaSubscript Baselin left-parenthesi up erNSubscript Baselin com amright-parenthesi tmesStarSetSartFactionleft-parenthesi up erNSubscript Baselin plustimestminus1right-parenthesi factorialOverl ft-parenthesi mplus1timesright-parenthesi Supersciptu perNSuperSubscript Superscipt lustBaselin EndFractionminusexpleft-bracketminusleft-parenthesi mti esplustimes1right-parenthesi SupersciptBaselin timestimesgam aoverba OverOversciptbarOversciptlamdaEndscriptsEndscriptsright-bracketnormalup erSigmaUndersciptnequals0Oversciptu perNSubscript Baselin plustminus1UndersciptOversciptEndscriptsStarFaction factorialStarBinomialOrMatrixup erNSubscript Baselin plustminus1Cho senE dBinomialOrMatrixOverl ft-parenthesi mplus1right-parenthesi Supersciptnplus1Baselin EndFractionleft-parenthesi Subscriptgam aoverba overba Baselin SupersciptlamdaB selin right-parenthesi Supersciptu perNSuperSubscript Superscipt lustimestminusnminus1Baselin EndSet

(8) Where in (8) at(Nr, m) is the coefficient ofm ,

expansion

of

m

(Nrt-1)ihne

.

Lemma 1:

Generally, when the average SNR per data symbol m is very 1), PTAS/MRC in (8) can be further simplified as the following large enough (e.g., m approximation, up erPSubscriptup erTup erAup erSslashup erMup erRup erCBaselinetimesequalstimesStartFraction1Overleft-parenthesi up erNSubscriptrBaselinefactorialright-parenthesi Superscriptup erKup erNSuperSubscript SuperscriptBaselineEndFractiontimesleft-parenthesi StartFraction2Superscriptup erC0Baselineminus1Overgam aoverbarEndFractionright-parenthesi Superscriptup erKup erNSuperSubscript Superscriptup erNSuperSubscriptrSuperscriptBaselinetimesplustimesotimesleft-parenthesi gam aoverbarSuperscriptup erKup erNSuperSubscript Superscriptup erNSuperSubscriptrSuperscriptBaselineright-parenthesi

(9) m■ In

For comparison, the outage probability for point-to-point (P2P) communication link where there is no multiuser diversity is derived as up erPSubscriptup erPBaseline2up erPBaselinetimes qualstimes1minuseSupersciptminusequalsUndersciptgam aOversciptlamdaEndscriptsBaselinetimes igma-sum ationUndersciptnequals0Oversciptup erNSubscriptrBaselineminus1EndscriptsUndersciptOversciptEndscriptsStarFactionleft-parenthesi SubscriptBaselineSupersciptBaseline qualsUndersciptgam aOversciptlamdaEndscriptsright-parenthesi SupersciptnBaselineOvernfactorialEndFraction

(10) It can be seen from (9) that the outage probability with multiuser diversity (MUD) is decreased by a factor of m . This is due to that, for multiuser

diversity, the transmitter will not only select the best antenna but also select the user who can achieve the largest post-processing SNR when using this antenna for transmission. Compared with point-to-point (P2P) link without multiuser diversity in (10) which is irrespective of the number of user K and the number of transmit antenna Nt, for the system with multiuser diversity, increasing the number of users will greatly decrease the outage probability. 3.2. Outage capacity The mean (expectation) value of effective SNR γs [as in (4) ] of the MIMO TAS/MRC system (with multiuser diversity) is calculated as, muSubscriptBaselineSubscriptsBaselinetimesequalstimesup erEleft-parenthesi gam aSubscriptsBaselineSubscriptBaselineright-parenthesi tmesequalstimesStarFactionup erZtimesgam aoverbarOverleft-parenthesi up erNSubscriptrBaselineminus1right-parenthesi factorialEndFractionsigma-sum ationUnderscriptmequals0Overscriptup erZminus1EndscriptsUnderscriptOverscriptEndscriptsleft-bracketleft-parenthesi negative1right-parenthesi SuperscriptmBaselineStarBinomialOrMatrixup erZminus1Cho semEndBinomialOrMatrixasterisktimes igma-sum ationUnderscript equals0Overscriptmleft-parenthesi up erNSubscriptrBaselineminus1right-parenthesi EndscriptsUnderscriptOverscriptEndscriptsaSubscript Baselinetimesleft-parenthesi up erNSubscriptrBaselinecom amright-parenthesi tmesStarFactionleft-parenthesi up erNSubscriptrBaselineplustright-parenthesi factorialOverleft-parenthesi mplustimes1right-parenthesi Superscriptup erNSuperSubscriptrSuperscript lustplus1BaselineEndFractionright-bracket

(11) Similarly, the second moment of γs is up erEleft-parenthesi gam aSubscriptsSuperscript2BaselineSubscriptSuperscriptBaselineright-parenthesi timesequalstimesStarFactionup erZtimesgam aoverbarsquaredOverleft-parenthesi up erNSubscriptrBaselineminus1right-parenthesi factorialEndFractionsigma-sum ationUnderscriptmequals0Overscriptup erZminus1EndscriptsUnderscriptOverscriptEndscriptsleft-bracketleft-parenthesi negative1right-parenthesi SuperscriptmBaselinetimesStarBinomialOrMatrixup erZminus1Cho semEndBinomialOrMatrixasterisksigma-sum ationUnderscript equals0Overscriptmleft-parenthesi up erNSubscriptrBaselineminus1right-parenthesi EndscriptsUnderscriptOverscriptEndscriptsaSubscript Baselinetimesleft-parenthesi up erNSubscriptrBaselinetimescom amright-parenthesi timesStarFactionleft-parenthesi up erNSubscriptrBaselineplustimest imesplustimes1right-parenthesi timesfactorialOverleft-parenthesi mtimesplustimes1right-parenthesi Superscriptup erNSuperSubscriptrSuperscript lustimest imesplus2BaselineEndFractionright-bracket

(12) Thus from (11) and (12) we can obtain the variance of effective system SNR γs for the MIMO TAS/MRC system, sigma Subscript s Superscript 2 Baseline times times equals times up er E times left-parenthesi gam a Subscript s Superscript 2 Baseline Subscript Superscript Baseline right-parenthesi minus left-bracket up er E left-parenthesi gam a Subscript s Baseline right-parenthesi right-bracket squared equals times up er E times left-parenthesi gam a Subscript s Superscript 2 Baseline Subscript Superscript Baseline right-parenthesi minus mu Subscript s Superscript 2

(13) Assuming that the channel capacity [as in (6)] can be approximated as a Gaussian process with mean µC and variance m , the cumulative distribution function (CDF) of the channel capacity is up er F Subscript up er C Baseline times left-parenthesi up er C right-parenthesi almost-equals 1 minus one-half times e r f c times left-parenthesi StartFraction up er C minus mu c Over StartRo t 2 EndRo t sigma Subscript up er C Baseline EndFraction right-parenthesi

(14) where erfc(•) is the complementary error function. According to [2], the q%-outage capacity is defined as the transmission rate that is guaranteed for (100 − q)%of the channel realizations, thus from (14) and after some calculations (for detailed calculations and derivations please refer to [11]), we get, up erCSubscriptqSuperscriptoutageBaselinetimesequalstimesmuctimesplustimes igmaSubscriptup erCBaselineStartRo t2EndRo terfcSuperscriptnegative1Baselinetimesleft-parenthesi 2minusqslash50right-parenthesi equalstimeslogSubscript2Baseline timesdotleft-bracketleft-parenthesi lntimesmuminusStartFractionsigmaSubscriptsSuperscript2BaselineOver2musquaredEndFractionright-parenthesi timesplustimesStartRo t2EndRo tStartFractionsigmaSubscriptsBaselineSubscriptBaselineOvermuEndFractiontimesStartRo t1minusStartFractionsigmaSubscriptsSuperscript2BaselineOver4musquaredEndFractionEndRo terfcSuperscriptnegative1Baselinetimesleft-parenthesi 2minusqslash50right-parenthesi right-bracket

(15)

:=1 + μs, take (11) and (13) into (15) we obtain the closed-form Where μ of the expression outage capacity for the multiuser MIMO TAS/MRC system. From (15) it is easily to see that the system outage capacity increases with the increase of mean (μs) of effective SNR and decreases with the increase of variance (m ) of the effective SNR. Thus in order to increase the outage capacity of the mul,

tiuser MIMO TAS/MRC system, we should find a scheme which has a good balance between the achieved average SNR and variance. Later in Section 4, through simulations we show that the number of receive antennas should be no more than that of the transmit antennas to achieve a higher outage capacity.

3.3. Error Performance Generally, the symbol error rate (SER) at a certain SNR γ for the commonly used signal constellations, including M-QAM, M-PSK, M-PAM, etc., can be written as the uniform expression, i.e., p Subscript Baseline Subscript s Baseline times left-parenthesi gamma right-parenthesi times equals times alpha times up er Q times left-parenthesi StartRo t beta gamma EndRo t right-parenthesi

(16) where α, β are determined by specific constellations [9], for example, for BPSK modulation, α = 1 and β = 2; for M-QAM, α = 4 and β = 3/(M − 1). For a certain average SNR m , the average SER is the symbol error rate in (16) over the PDF of γ in (5), thus, we evaluate the integral as, up erPSubscriptsBaselineSubscriptBaselinel ft-parenthesi gam aoverbar ight-parenthesi timesequalstimesStartFractionalphaup erZOverleft-parenthesi up erNSubscriptrBaselineminus1right-parenthesi factorialEndFractionsigma-sum ationUnderscriptmequals0Overscriptup erZminus1EndscriptsUnderscriptOverscriptEndscriptsleft-parenthesi negative1right-parenthesi SuperscriptmBaselinetimesStartBinomialOrMatrixup erZminus1Cho semEndBinomialOrMatrixsigma-sum ationUnderscript equals0Overscriptmtimesleft-parenthesi up erNSubscriptrBaselineminus1right-parenthesi EndscriptsUnderscriptOverscriptEndscriptsaSubscript Baselinetimesleft-parenthesi up erNSubscriptrBaselinetimescom amright-parenthesi timesdotup erISubscriptup erNSubSubscriptrSubscriptBaselinetimesleft-parenthesi betacom amcom atright-parenthesi

(17) The basic integral INr(β,m,t) is given by, up erISubscriptup erNSubSubscriptrSubscriptBaselinetimesleft-parenthesi betacom amcom atright-parenthesi tmesequalstimesleft-parenthesi t imesplustimesup erNSubscriptrBaselineminus1right-parenthesi factorial eft-bracketSartFaction1minusmuSubscriptmBaselineOver2timesleft-parenthesi mtimesplustimes1right-parenthesi EndFractionright-bracketSuperscript imesplustimesup erNSuperSubscriptrSuperscriptBaselinetimes igma-sum ationUnderscriptnequals0Overscript plusup erNSubscriptrBaselineminus1EndscriptsUnderscriptOverscriptEndscriptsleft-parenthesi SuperscriptBaselinenOverscript plusup erNSubscriptrBaselineminus1timesplustimesnEndscriptsright-parenthesi left-parenthesi StarFaction1plusmuSubscriptmBaselineOver2EndFractionright-parenthesi Superscriptn

(18)

Where by definition, .m Lemma 2: for

in (17)

can

be

large average SNR ( m generally simplified as,

(also see [9], Section 14.4.1) »

1), the average symbol error probability

up erPSubscriptsBaselineSubscriptBaselinetimesleft-parenthesi gam aoverbar ight-parenthesi timesalmost-equalsalphaup erKup erNSubscript Baselinetimesleft-bracketStartFraction1Overleft-parenthesi up erNSubscriptrBaselineminus1right-parenthesi timesfactorialEndFractionright-bracketSuperscriptup erKup erNSuperSubscript SuperscriptBaselineStartFractionleft-parenthesi 2timesup erKup erNSubscript Baselineup erNSubscriptrBaselinetimesminus2up erKup erNSubscript Baselinetimesplustimes1right-parenthesi timesfactorialOverleft-parenthesi up erKup erNSubscript Baselinetimesup erNSubscriptrBaselinetimesminusup erKup erNSubscript Baselinetimesplustimes1right-parenthesi factorialEndFractionleft-parenthesi StartFraction1Over2betagam aoverbarEndFractionright-parenthesi Superscriptup erKup erNSuperSubscript Superscriptup erNSuperSubscriptrSuperscriptminusup erKup erNSuperSubscript Superscript imesplustimes1

plustimesotimesleft-parenthesi gam aoverbarSuperscriptleft-parenthesi up erKup erNSuperSubscript Superscriptup erNSuperSubscriptrSuperscripthyphenup erKup erNSuperSubscript Superscript imesplustimes1timesright-parenthesi Baselineright-parenthesi

(19) Proof: see the Appendix.■

From this

approximated expression, it can be

to D = (KNtNr

—

KNt + 1) can be

seen that a diversity order equals and what’s more, for very large achieved;

number of receive antenna Nr, D = (KNtNr KNt + 1) ≈ (KNtNr) i.e., a diversity order of D = (KNtNr) can be extracted. Also from this equation it is shown that in multiuser MIMO TAS/MRC systems the number of users K will provide the same performance as that of the transmit antenna Nt, in other words, users can -

be equivalent to "virtual” transmit antennas, this is just the source of the inherent multiuser diversity (MUD). Thus in MIMO system design, we can efficiently utilize the inherent diversity in multiuser MIMO system to bring the same performance instead of increasing the number of transmit antennas.

4. Numerical Investigations In this

section, we give the numerical investigations regarding the outage probability,

outage capacity and symbol error rate performance in multiuser MIMO TAS/MRC system. In all the figures, the exact analysis and approximated results derived in Section 3 are presented, which are plotted in solid and dotted lines, respectively. Figure 2 compares the outage probability for different antenna configurations, it

seen that the scheme with multiuser diversity (PMP link) obtains signiflower icantly outage probability than that without multiuser diversity (P2P link), which is due to the transmit antenna selection and multiuser diversity gain. For multiuser diversity, Figure 2 also shows that when transmit antenna Nt is large, more diversity gain can be obtained, e.g., for multiuser diversity system, (Nt = 4; Nr = 1) achieves 2dB gain more than (Nt = 3; Nr 1) system. This is because that a large number of Nt provides more selection possibilities and the scheduler will have more chance to select the ’best’ transmit antenna which brings large post-processing SNR. Figure 3 (a) and (b) show the impact of number of user K and number of transmit antenna Nt on 5%-outage capacity (q = 5). respectively. It can be observed that the performance increases with the increase of number of transmit antenna (Nt) or users (K). What’s more, both from theoretical analysis and simulation results, the can

be

=

Figure 2. Outage probability vs. average SNR for different antenna configurations with and without multiuser diversity. (number of user K = 2)

Figure 3. Outage capacity vs. average SNR of MIMO TAS/MRC system for different number of (a) user K; (b) transmit antenna Nt

Figure 4. Outage capacity vs. MIMO antenna configurations for different average SNRs. (number of user K = 2)

number of transmit antenna (Nt) and users (K) bring the same influence on the outage capacity. This result gives us an idea that to get a higher outage capacity performance, instead of increasing the number of transmit antennas Nt which is very expensive in practice, we can efficiently utilize the multiuser diversity inherent exists in multiuser system to obtain the same performance gain. Figure 4 shows the 5%-outage capacity versus different MIMO antenna configurations. The total number of antennas is set as Nt + Nr 6. It can be seen that with the increase of transmit antenna Nt (so decrease of receive antenna Nr), the outage capacity first increases and when Nt exceeds a certain number (e.g., Nt = 2, Nr = 4), the outage capacity begins to decrease! For a certain number of user K, a large number of transmit antenna Nt brings large antenna selection gain; for maximal-ratio combining (MRC) at the receiver, a large number of receive antenna Nr brings more combining gain. Also as shown in (15) the outage capacity depends on the mean (expectation) and variance of the effective SNR; with the increase of Nt and the 2*4 brings the decrease of Nr (e.g., 1*5 → 2*4→ 3*3→ 4*2 → 5*1), Nt*Nr maximum sum of antenna selection gain and combining gain, thus the maximum outage capacity is achieved. In fact, for antenna configurations: 1*5, 2*4 and 3*3, the outage capacity varies very little. This result shows that in multiuser MIMO —

,

=

Figure 5. (a) Impact of number of user K on SER of BPSK for MIMO TAS/MRC 1*3 system; (b) Impact of number of transmit antenna Nt on SER of QPSK (Nr = 2,K = 2)

Figure 6. Comparison of SER of BPSK modulation for different MIMO configurations (Nt + Nr = 4)

TAS/MRC system, to achieve a higher outage capacity, the number of transmit antennas should be no more than that of the receive antennas, i.e., Nt ≤ Nr. Comparing Figure 5 (a) &(b) , we can easily see that increasing the number of users K will provide the same performance as that of the transmit antenna Nt, that is to say, users can be viewed as “virtual” transmit antennas, which is the source of the inherent multiuser diversity (MUD). In the system design, we can and should efficiently utilize the inherent diversity to bring the same performance instead of increasing the number of antennas. Figure 6 depicts the symbol error rate of BPSK for a total number of antennas: Nt + Nr = 4. It is seen that the best performance is obtained for the MIMO TAS/MRC antenna configuration — Nt = Nr = 2. For a certain number of user K (in this case, K = 1), a large number of transmit antenna Nt brings about large antenna selection gain; for maximal-ratio combining (MRC) at the receiver, a large number of receive antenna Nr brings more combining gain. Since there’s a limit of the total number of antennas — increasing Nt will inevitably reduce Nr, while increasing Nr will inevitably reduce Nt — there’s a trade-off between the number of transmit and receive antennas. Through simulation analysis, we show that the

largest sum of combined antenna selection gain and combining gain is obtained by equally distributing antennas over transmit and receive side.

5. Conclusions Multiuser diversity is a kind of diversity inherent exists in multiuser systems. This paper gives a comprehensive study about multiuser diversity (MUD) in MIMO systems. Specifically, a framework is presented to analyze the performance of multiuser diversity. Through theoretical analysis with ideal feedback information, we derive the closed-form expressions of outage probability, outage capacity and average symbol error rate from a multiuser system perspective for the multiuser MIMO transmit antenna selection with maximal-ratio combining (TAS/MRC) system, by which we show how and with what characteristics antenna selection gains, MIMO antenna configurations, multiuser diversity and fading gains impact on the system performance. Multiuser diversity is of huge benefits to the multiuser MIMO systems. This paper reveals the theoretical characteristics of multiuser diversity in multiuser wireless networks with multiple antennas and demonstrates the correctness of the theoretical analysis through computer simulations, which helps to design efficient scheduling methods for the multiuser MIMO TAS/MRC system. In the design of MIMO system, we can efficiently utilize the inherent diversity to improve the performance instead of increasing the number of antennas.

Appendix Proof of Lemma 2 In

large

about

average effective SNR

regime (i.e., m

»

1),

we

have such

approximations

m , StartFraction 1 minus mu Subscript m Baseline Over 2 times left-parenthesis m plus 1 right-parenthesis EndFraction almost-equals StartFraction 1 Over 2 beta gamma overbar EndFraction times and StartFraction 1 times plus times mu Subscript m Baseline Over 2 EndFraction almost-equals 1 times

(20) Using these two approximations, the integral function INr(β,m,t) in (18) can be further simplified as, up erISubscriptup erNSubSubscriptrSubscriptBaselinetimesleft-parenthesi betacom amcom atright-parenthesi almost-equals eft-parenthesi t imesplus p erNSubscriptrBaselineminus1right-parenthesi factorial eft-parenthesi StarFaction1Over2betag m aoverba EndFractionright-parenthesi Superscipt plus p erNSuperSubscriptrSupersciptBaselinetimes igma-sum ationUndersciptnequals0Overscipt plus p erNSubscriptrBaselineminus1EndscriptsUndersciptOversciptEndscriptsleft-parenthesi nOverscipt plus p erNSubscriptrBaselineminus1plusnEndscriptsright-parenthesi equalsStarFactionleft-parenthesi 2t imesplustimes2up erNSubscriptrBaselineminus1right-parenthesi factorialOverl ft-parenthesi t imesplustimesup erNSubscriptrBaselineright-parenthesi factorialEndFractionStarFaction1Over2betag m aoverba EndFractionright-parenthesi Superscipt imesplustimesup erNSuperSubscriptrSupersciptBaseline

(21)

Where in (21) we use such equation as follows, sigma-sum ation Underscript n equals 0 Overscript plus up er N Subscript r Baseline minus 1 Endscripts Underscript Overscript Endscripts left-parenthesi Superscript Baseline n Overscript times plus times up er N Subscript r Baseline minus 1 times plus times n Endscripts right-parenthesi times equals times StartBinomialOrMatrix 2 times t imes plus times 2 up er N Subscript r Baseline Subscript Baseline minus 1 Cho se t imes plus up er N Subscript r Baseline EndBinomialOrMatrix

(22) Take these approximations (20)&(21) into (17), we obtain the average symbol error rate formula as in (19), uperPSubscriptsBaelin SubscriptBaselin eft-parenthsi gam aoverba right-parenthsi almost-equals phauperZleft-bracketSartFaction1Overlft-parenthsi uperNSubscript Baselin tmesminus1right-parenthsi factorialtmesEndFractionrght-bracketSupersciptuperZBaselin tmesStarFactionleft-parenthsi 2uperZuperNSubscript imesBaelin tmesminus2uperZtimesplus1right-parenthsi factorialOverlft-parenthsi uperZuperNSubscript Baselin tmesminus perZtimesplus1right-parenthsi factorialEndFraction meslft-parenthsi StarFaction1Over2betagm aoverba EndFractionrght-parenthsi SupersciptuperZuperNSuperSubscript Supersciptminus perZplus1timesBaelin plusotimeslft-parenthsi gam aoverba Supersciptminusleft-parenthsi uperZuperNSuperSubscript Supersciptminus perZtimesplustimes1right-parenthsi Baselin rght-parenthsi tmes qualstimesalph uperKuperNSubscript Baselin eft-bracketSartFaction1Overlft-parenthsi uperNSubscript Baselin minus1right-parenthsi factorialEndFractionrght-bracketSupersciptuperKuperNSuperSubscript SupersciptBaselin StarFactionleft-parenthsi 2uperKuperNSubscript Baselin uperNSubscript Baselin hypen2uperKuperNSubscript Baselin tmesplustimes1right-parenthsi factorialOverlft-parenthsi uperKuperNSubscript Baselin uperNSubscript Baselin minus perKuperNSubscript Baselin tmesplustimes1right-parenthsi factorialEndFraction meslft-parenthsi StarFaction1Over2betagm aoverba EndFractionrght-parenthsi SupersciptuperKuperNSuperSubscript SupersciptuperNSuperSubscript Supersciptminus perKuperNSuperSubscript Superscipt lus1

plustimesotimesleft-parenthesi gam aoverbarSuperscriptminusleft-parenthesi up erKup erNSuperSubscript Superscriptup erNSuperSubscriptrSuperscriptminusup erKup erNSuperSubscript Superscript imesplustimes1right-parenthesi Baselineright-parenthesi

(23)

Acknowledgement This work is supported by the National Basic Research Program of China (973 Program) under Grant 2007CB310602.

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On MIMO Channel Characterization for Future Wireless Communication Systems H. Farhat, R. Cosquer, G. El Zein Institut d’Electronique et de Télécommunications de Rennes (IETR/UMR CNRS 6164) INSA-20 av. des Buttes de Coësmes, CS14315, 35043 RENNES CEDEX, FRANCE. Phone: (+33) 2 23 23 86 04, Fax: (+33) 2 23 23 84 39 E-mail: [email protected] Abstract. The use of MIMO (Multiple-Input Multiple-Output) techniques for the future wireless systems is a good solution to increase data rates, and quality of service. The performances of these systems are very dependent on the propagation channel between the emitter and receiver sites. That makes the spatio-temporal characterization and modeling of the channel very crucial in this context. This paper highlights different aspects concerning the MIMO propagation channel. At first, we give a brief overview on the modeling and the characterization of the MIMO channel. Thereafter, we present a realized wideband MIMO channel sounder at 2.2 and 3.5GHz. Different architectures of antenna arrays are presented. The two high resolution algorithms ESPRIT and SAGE are used to have more resolution and accuracy on measurement data. Antenna arrays beam patterns calibrations in anechoic chamber are shown. Finally, some MIMO propagation measurement results are illustrated. Keywords: Wireless Telecommunications, 4G, MIMO Channel Sounding, Antenna Arrays Design and Calibration, Double Directional Channel Measurements.

1. Introduction In the last decade, the world of telecommunications has known an important development, driven by the success of 2G mobile communications systems such as GSM. The services offered by 3G and 4G mobile systems will be extended to data transmission and multimedia applications which increase the necessity of very high data rates and better service quality. Among the techniques adopted for future wireless systems, MIMO shows that it is able to increase the channel capacity. For example, MIMO technology was adopted by the IEEE 802.11n and IEEE 802.16e standards. In fact, by using several antennas at both communication link sides, these systems exploit the spatial dimension to transmit information. The theoretical capacity study of MIMO systems was first presented in the pioneer work of Winters [1], then the works in [2], [3] express this capacity for iid Gaussian channel from an information theory point of view. Then many other studies were conducted [4–8] to estimate the obtained capacity with different assumptions concerning the propagation channel. All these studies clearly show that the performance of MIMO systems is very dependant on the propagation channel, and this reality made characterization and modeling of the mobile radio channel very crucial. In this context, it is very important to model this MIMO channel in the

DOI: 10.1201/9781003336853-22

On MIMO Channel Characterization realistic way to then estimate the obtained capacity. Recently, many give an overview on the advances done for MIMO channel characterization and modeling, were published. They conclude that more propagation measurement results are necessary to understand in depth

most

possible

state of the art papers and books [9 12] those -

all

phenomena that can affect MIMO systems performances. This paper is organized as follow. In Section 2, we introduce the MIMO principle. Section 3 presents a brief overview on the MIMO propagation channel modeling. Section 4 addresses measurement techniques used to characterize the MIMO propagation channel and describes the developed channel sounder. In Section 5, we present different antenna arrays architecture developed at the 2.2 and 3.5 GHz frequencies and the high resolution algorithms used in propagation data processing. Section 6 gives some measurement results. Section 7 concludes this paper and proposes some perspectives of this work.

2. MIMO Wireless Communication Systems Today, wireless access networks show limits in terms of data rate, quality of service (QoS) and spectral efficiency. Many applications are concerned such as wireless local area networks (WLAN), wireless local loop (WLL) and future generations of mobile radio systems (3G, 4G and beyond). For several years, efforts have been made to improve the design of the existing systems. In fact, the trend to increase data rates will most probably continue to reach 100 Mbps considering a moderate mobility, and up to 1 Gbps for a reduced mobility. The MIMO technology appears as a new concept to fulfill those specifications. The MIMO principle can be defined simply. Since time and frequency domains processing are pushed to their limits, the space domain can be exploited. The main idea is to transmit multiple streams of data on multiple antennas at the same frequency. Usually, multiple receiving antennas are considered to improve the system performance (Figure 1). In an ideal case, it can be shown that the channel capacity grows linearly with the number of transmitting (Tx) and receiving (Rx) antennas [3]. This technique can be viewed as a generalization of space diversity and smart antennas [13]. It assumes a channel rich in multiple paths in order to exploit independent transmission channels between the Tx and Rx antennas. This transmitting and receiving structure can be modeled using a matrix representation of the channel. Information theoretic considerations allow highlighting that two fundamental mechanisms are at stake in the process of transferring information: diversity (reception of multiple decorrelated copies of the same transmitted information, by combining, allow to combat channel fading), and multiplexing (reception of multiple independent symbols of information to increase the channel capacity). The structure of the propagation channel places a tradeoff between the two types of gain. The really large improvement in link reliability and/or data rates, and predicted by information theory relies on a fine knowledge of the propagation

3. MIMO Channel Modeling

Figure 1. (a) ULA 4 elements TX and integrated electronic components at 3.5 GHz; (b) URA 16 elements (c) 16 elements UCA beam pattern measurements in anechoic chamber for vertical and horizontal polarization at 3.5GHz; (d) 16 elements UCA electronic components integration Rx at 2.2 GHz;

phenomena. Such knowledge makes it possible to choose the most appropriate coding/modulation scheme for a given environment. Transmitting and receiving antenna arrays have to be carefully designed to maximize the channel rank, i.e., the number of eigenmodes available for communication. In this case, correlation and dispersion measurements of channel parameters play a central role.

3. MIMO Channel Modeling The radio propagation of electromagnetic waves from a transmitter to a receiver is characterized by the presence of multipath due to various phenomena such as reflection, refraction, scattering and diffraction. Several methods of classification of the MIMO models are proposed in the literature [9], [12], [14], [15]. In general, we distinguish between deterministic and stochastic models. 3.1. Deterministic Models Deterministic models are based on a fine description of a specific environment. In this class, two approaches can be identified: the site-specific ray tracing and techniques based on the processing and exploitation of measured data. At first, ray-tracing models, based on optical approximations, need complete geometrical and electromagnetic specifications of the simulated environment. They enable to estimate the channel characteristics with a good accuracy, if the environment modeled is not too complex. Moreover, other models can be used which are based on the Maxwell’s equations; they require much computation time. Secondly, another type of models use recorded measurement data which can be playback by means of computer. Thus, the measurement campaigns of the propagation channel enable to extract different characteristic parameters of a specific environment. But these parameters appears very specific to experimental conditions

including the environment and the antenna array; but, the simulations need great memory resources. 3.2. Stochastic Models The stochastic models aim to describe the channel parameters by random laws. In this category, we have geometrically-based, correlation-based and parametric stochastic models. Recently, some standardized models, as the COST 273 channel model [ 11 ], and the WINNER II MIMO channel models [ 16], use the MIMO propagation channel clustering concept. These models are geometry based on the one hand and stochastic on the other, and seem to be good and general models.

4. MIMO Channel Characterization The study of wave propagation appears as an important task when developing a wireless system. The analysis is usually made in the time domain, which allows measuring the coherence bandwidth, the coherence time, the respective delay spread, and Doppler spread values.

Also, coherence distance, correlation distance, and wave direction spread are used to highlight the link between propagation and system in the space domain. For broadband systems, the analysis of both path loss (estimation of cell coverage and carrier-to-interference ratio) and impulse response (estimation of the wideband channel characteristics) are required. Therefore, an accurate description of the spatial and temporal properties of the channel is necessary for the design of broadband systems, and also for the choice of the network topology. 4.1. Measurement Techniques In practice, two main approaches can be used in order to characterize the propagation channel. The first approach directly measures the time-variant MIMO channel coefficients matrix simultaneously in the time, frequency and spatial domains. However, this method presents some limitations as the antenna arrays used during measurement must be assumed for the simulations. The second approach, adopted in our works, is based on the processing of the different time-variant transfer function and generally referred to as double directional channel measurements [17]. It tends to estimate the multipath parameters (direction of departure DOD, direction of arrival DOA, time delay, Doppler shift, polarization and amplitude) by using high resolution multidimensional MIMO sounding techniques. With the polarization parameters knowledge, this approach excludes the antenna and electronic influences from the measured results and thus, it can be generalized easily. Based on this approach, a wideband MIMO channel sounder was developed at IETR.

A variety of MIMO channel sounders were developed [18-20] to characterize multiple paths parameters like DOA ( Direction Of Arrival), DOD ( Direction Of Departure), in addition to delay, Doppler, polarization and path loss. The majority of propagation measurement results obtained with these channel sounders are in the 5 GHz bandwidth.

At our laboratory, a wideband MIMO channel sounder was developed at IETR/INSA [21], initially it operates at 2.2 GHz RF (Radio Frequency) for 3G and WLAN applications and was also upgraded to 3.5 GHz RF to cover other wireless applications like WiMAX. It uses a periodic transmit signal based on the spread spectrum technique. This channel sounder offers an 11.9 ns temporal resolution with 100 MHz sounding bandwidth. Other sounding bandwidths can be used like 50, 25 and 12.5 MHz in environments were the temporal resolution can be reduced. Different impulse response lengths (µs) can be recorded (10.23, 5.11, 2.55 ...). The best dynamics obtained is 50 dB on the impulse response for the 1023 code length. The AGC (Automatic Gain Control) unit is divided into two parts, one at 2.2 or 3.5 GHz (50 dB) and the second permits a 45 dB gain at the IF (Intermediate Frequency) at 250 MHz. The LO (Local Oscillator) units generate signals at 2.45 and 3.75 GHz and then a mixer is used to obtain the two desired frequencies. The synchronization between the emitter (Tx) and the receiver (Rx) is achieved with highly stable 10 MHz rubidium oscillators. A system calibration is performed. We connect the Tx RF output to the Rx RF input through appropriate variable attenuators and the calibration is performed for all AGC values with a 5 dB step. The next section describes the developed antenna arrays.

5. Antenna Arrays Design and Calibration 5.1. Antenna Arrays Design For the DOA and DOD measurements, different techniques exist like the rotation of narrow-beam antenna, the synthetic aperture method or the parallel channels at emitter and receiver. We choose the RF-switching technique at the emitter Tx and receiver Rx arrays. Different antenna arrays architectures were developed depending on the measurements type and environment. At the emission, we developed two ULAs (Uniform Linear Array) at 2.2 and 3.5 GHz of four active elements each, and two passive edge elements to reduce the influence of environmental reflections and to avoid any beam pattern discontinuity. At the emitter arrays, we integrate power amplifiers after the switch to increase transmitted power. As an example, Figure 1(a) presents the Tx array at 3.5 GHz and the integrated electronic components. At the receiver arrays, we integrate LNAs (Low Noise Amplifiers) just after the antennas to have better measurements dynamic. This integration of LNAs permits us to reduce the receiver noise figure to 4 dB.

Figure 1(b) presents the 4x4 URA (Uniform Rectangular Array) at 2.2GHz; it contains 16 active elements and 48 edge elements. It is used in indoor and outdoor to indoor environments to estimate DOA in the azimuth and elevation planes. Figure 1(c) presents the 16 elements UCA (Uniform Circular Array) at 3.5 GHz and the integrated electronic components ( Figure 1(d) ). It is used in indoor and outdoor to indoor environments to estimate DOA in the azimuth and elevation planes. 5.2. Antenna Arrays Calibration In order to

improve multipath propagation parameters estimation, we used the ESPRIT (Estimation of Signal Parameters via Rotational Invariance TechUnitary niques) algorithm [22 ] with ULAs and URAs because it is the best high resolution algorithm adapted for planar arrays [23 ]. The ESPRIT algorithm is very sensitive to antenna arrays imperfections, since it relies on identical beam patterns. To apply this algorithm on measurement data, a calibration procedure based on [24-26] was applied on measured beam patterns in anechoic chamber to obtain more accurate results and to reduce parameters estimation errors [27 ]. As an example, we present the calibration of the ULA Tx array at 3.5 GHz. Figure 2(a & b ) show respectively the 4 elements ULA Tx beam patterns ripple at 3.5 GHz before and after calibration. In the ULA geometry case (M elements spaced by d), in ideal case, if a single planar wavefront with complex attenuation γ, from the azimuthal direction θv impinges. The array response vector results in x = aγ, where a is the array steering vector: (1) a times left-parenthesi theta Subscript upsilon Baseline right-parenthesi times equals times left-bracket 1 times e Superscript minus j Baseline 2 pi StartFraction d Over lamda EndFraction times ine theta Super Subscript upsilon Superscript Baseline times elipsi e Superscript negative j times 2 times pi tmes left-parenthesi up er M hyphen 1 right-parenthesi times StartFraction d Over lamda EndFraction times ine theta Super Subscript upsilon Superscript Baseline right-bracket Superscript up er T Baseline

In the real case, the measured array response vector becomes: xm

=

Kaγ +

(2) n

where n is the additive noise and K (M × M) is the error matrix that describes the array imperfections.

Figure 2. (a) 4 elements ULA Tx beam patterns ripple at 3.5 GHz; (b) 4 elements ULA Tx beam patterns ripple reduced after calibration

The main

of K matrix contains the amplitude and phase errors of the K-1 algorithm calculates the correction matrix Kcal that removes the systematic error if applied to the array output. The proposed algorithm to estimate Kcal is based on the idea that for an errorfree array, a set of orthogonal null steering vectors c exists

diagonal

antennas. The calibration

(1 ≤ μ ≤ M a(θv).

—

=

1). They span the equivalent nullspace of the reference source

vector

The double directional propagation measurements performed with ULAs or URAs permits us to obtain the channel properties for a 120◦ sector, and to obtain a full 360◦ azimuth we have to rotate the array of 3 × 120◦, and that increase the measurements time. For that aim we developed 16 elements UCA (Uniform Circular Array) Rx at 3.5 GHz (Figure 1(c)) to obtain full azimuthal DOA instantly. To estimate multipath propagation parameters with the UCA array, we developed the high resolution algorithm SAGE [28] because it is the best algorithm adapted for these antenna arrays architectures [29]. The UCA beam patterns measurement where performed in anechoic chamber for the horizontal and vertical polarizations (Figure 1(c)) to estimate the DOA in the azimuth and elevation planes with ambiguity above and below the plane of the array.

6. Measurement results As an example of MIMO propagation measurement results obtained with our channel sounder, we present the measured double directional response in outdoor environment with two configurations in LOS (Line Of Sight) and NLOS (Non LOS). The measurements were performed at 2.2 GHz, using at the emission site 4 elements ULA and 8 elements ULA at the reception. The antenna arrays are rotated 9 times to obtain 360° full azimuthal spatial responses at the two sites. The high resolution algorithm unitary ESPRIT was applied on measurement data. Figure 3(a) presents the spatial responses at emitter and receiver in the LOS configuration. In this case, we can notice that the maximum path power is observed when the two arrays are faced. Figure 3(b) presents the spatial responses at emission and reception site in the NLOS configuration, where the emitter is placed in height in comparison with the receiver position. Here, we can notice that the DODs are concentrated in one dominant direction to the receiver and the DOAs arriving at the receiver.

are

distributed

along

the routes

7. Conclusion This paper covered some aspects concerning MIMO channel characterization and modeling. In particular, a dual-band MIMO channel sounder is presented, and the used antenna arrays are briefly described. Some propagation measurement results are given. It follows that, in the MIMO context, the knowledge of the spatiotemporal channel response appears essential for future wireless systems simulation.

Figure 3. DOD and DOA in LOS (a) and NLOS (b) configurations

In order to obtain more realistic MIMO channel models, extensive measurement campaigns are needed, considering different environments and frequency bands.

Acknowledgments This work is part of Techim@ges and Palmyre projects which are supported by “Region Bretagne” and “Le Pôle de Compétitivité Images et Réseaux”.

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C\ Taylor & Francis ~

Taylor&FrancisGroup http://taylo ra ndfra n ci s.com

Modelling and Analysis of Capacity-Optimal Indoor MIMO Line-Of-Sight Wireless Channels Christian A. Hofmann and Andreas Knopp Institute for Communications Engineering at the Munich University of the German Bundeswehr Abstract. Line of Sight channels are often treated to be generally less appropriate for MIMO applications, providing only low capacity gains due to their inherent channel correlation. Contrarily, it is shown that with optimised antenna arrangements even the maximum multiplexing gain can be achieved in LOS channels. It is proven that the NLOS signal parts are not harmful to the capacity of LOS optimised channels and even beneficial for channels with a suboptimal antenna setup. Channel measurement results at 2.4 GHz are taken into account showing promising results for the channel capacity in indoor LOS environments. An essential prerequisite for those results is an antenna spacing larger than half-wavelength. An analysis on the link level performance justifies the effort of optimizing the antenna setup by a BER analysis. Keywords: MIMO, channel capacity, LOS channels, indoor MIMO channel measurements, bit error rate.

1. Introduction Multiple Input Multiple Output (MIMO) communication systems have attracted high interest during the last decade, since they have been shown by the initial contributions [ 1 ],[ 2 ] to promise high data rates. The characterization and modelling of the underlying MIMO wireless channel is still an important field of investigation. Especially in the course of the developments for the IEEE 802.11 n standard for Wire—

less Local Area Networks (WLAN), the indoor wireless channel has moved into the focus of analysis. In indoor scenarios the signal propagation is characterized by multiple paths forming a frequency selective multipath channel. The presence of a Line of Sight (LOS) signal part adjacent to the non Line of Sight (NLOS) parts marks a special case of an indoor channel. At times the LOS component is considered to be harmful to the performance of the MIMO channel, while other contributions prove the high capacity of such channels. The LOS channel is characterized by a transmitter (Tx) and a receiver (Rx) located within the same room with no obstacles in between that are capable to influence the channel characteristics. A LOS MIMO channel can be found in various applications like large conference rooms or lobbies in hotels or airports and also industrial applications in production halls are imaginable. With upcoming outdoor MIMO applications like WiMAX (IEEE 802.16), the theory presented in this contribution becomes also important for outdoor systems.

DOI: 10.1201/9781003336853-23

Modelling and Analysis of Indoor MIMO LOS Wireless Channels

2. Indoor LOS MIMO Channel Characteristics The important impact of the channel characteristics on the capacity gain of MIMO channels was already revealed by Telatar in his initial contribution [ 1 ]. He showed the Rayleigh fading channel, which for sufficiently large antenna spacing provides independently and identically distributed entries within the channel transfer matrix, to be a very

appropriate communication channel for MIMO applications. It offers capacity gains close to the theoretical optimum. First field trials [3 ] in Rayleigh fading scenarios showed promising results due to the rich scattering environment, which is a basic prerequisite for a Rayleigh channel. It was figured out that transmission channels with fading correlations encounter a reduced performance compared to uncorrelated Rayleigh channels [4 ]. The quality of the MIMO channel can be derived from the eigenvalue profile of the channel transfer matrix (CTM). An optimum eigenvalue profile with equally strong eigenvalues delivers a maximum channel capacity. A lower bound for the capacity is given by the so called “keyhole” channel, where only one eigenvalue is different from zero [ 5 ]. Dealing with LOS channels, a correlated CTM must be taken for granted. As the LOS transmission paths have to be described deterministically instead of applying a stochastic channel model, the propagation paths between different MIMO antenna elements are obviously correlated. Thus, the LOS MIMO channel is often supposed to be an inappropriate choice in contrast to the NLOS channel with less correlation [6]. This statement only holds true if the CTM is power-normalized for the purpose of comparison while the path loss is neglected. In a real world scenario, presuming identical Tx-Rx distance, the LOS channel will outperform the NLOS channel in most cases due to its lower path loss. Its benefit in receive power results in a much higher signal to noise ratio (SNR) at the receiver which consequentially leads to higher capacities. The Rayleigh fading property of a MIMO channel is mainly caused by a rich scattering environment. This means, that numerous multipath components (MPCs) from uncorrelated scattering impinge at the receiver and interfere each other, leading to uncorrelated entries in the CTM. Contrarily, in indoor scenarios MPCs mainly arrive as reflected signals from the surrounding walls, the floor and the ceiling. Here only few deterministic MPCs impinge at the receiver, and the entries in the CTM high channel

are therefore correlated [ 5 7 ]. The indoor channel is assumed to be time invariant for short durations due to the low mobility in indoor scenarios. Especially for the length of typical signal burst durations this statement holds true. ,

It is well known from early investigations [8] on the inter antenna element spacing of multi element antenna systems that in Rayleigh fading channels it is sufficient to choose an antenna spacing of at least 0.4λ, where λ denotes the centre wavelength of the transmission band. Consequentially, the uniform linear antenna array (ULA) with half-wavelength element spacing has become a standard MIMO antenna assembly which can be easily implemented. As a fundamental contrast to this statement it has recently turned out, that a fixed antenna spacing of halfwavelength is the most limiting factor for the exploitation of the LOS signal component in terms of high spatial multiplexing. This result was first indicated by indoor

4. Modelling the LOS MIMO Channel

measurements in [9] and [10] where the authors suggest a generally larger ULA antenna spacing to improve the capacity gain of LOS channels.

3. MIMO Channel Capacity According to [1] and [2] for a MIMO system consisting of N transmit antennas and M receive antennas, if uncorrelated transmit signals and equal power at each Tx antenna are presumed, the time invariant channel spectral efficiency is calculated up er C times equals times StartFraction 1 Over up er B EndFraction integral Underscript up er B Endscripts log times Subscript 2 Baseline left-bracket det imes left-parenthesi up er I Subscript up er M Baseline times plus times StartFraction sigma Subscript x Superscript 2 Baseline Over sigma Subscript eta Superscript 2 Baseline EndFraction times up er H times left-parenthesi f right-parenthesi times up er H Superscript normal up er H Baseline times left-parenthesi f right-parenthesi right-parenthesi right-bracket normal d f times period

C denotes the channel capacity normalized by the transmission bandwidth (unit 1 for a frequency selective MIMO channel in the absence of channel the Tx. Here, B denotes the transmission bandwidth, IM is the idendenote the mean transmit power allocated to each transmit

[Bit/sec/Hz]) knowledge at tity matrix, m

antenna and the noise power per receive antenna, respectively. Moreover HH(f) abbreviates the complex conjugate transpose of the channel transfer matrix H(f), in most papers the signal to noise and f denotes the frequency. Instead of m ratio (SNRRx) at the receiver input is used. Working with the SNRRx means that the CTM has to be power normalized to a certain power norm, which is equivalent ,

the channel path loss. By replacing the SNRRx with m it is the CTM unchanged with respect to the incorporated path loss. This strategy appears to best represent the physical nature of the channel as it incorporates both capacity-affecting effects: the path loss as well as the eigenvalue profile of the channel transfer matrix. Including the path loss into the capacity calculation is an essential prerequisite for a fair evaluation of the LOS channel in comparison

factoring out possible to leave to

to NLOS channels.

4. Modelling the LOS MIMO Channel 4.1. Spherical Wave Model The most crucial aspect for the description of the LOS signal in MIMO communications is the applied model of wave propagation. The spherical wave model generally is the physically correct model of wave propagation. A wave front propagates as a sphere with the antenna element in its centre. The plane wave model is often applied for very large Tx-Rx distances, where the wave fronts can be approximated as planes. It is assumed that the waves arrive as parallel planes at the receiver site. This assumption is valid for large Tx-Rx distances compared to the distance of two observation

1 the terms “capacity” and “spectral efficiency” are used synonymously, here.

points at the receiver as it is definitely the case in outdoor wireless communications. In indoor scenarios, where this condition is not always fulfilled, the occurring error has to be regarded [9]. The following paragraph will actually prove that the plane wave model is an inadequate choice for the calculation of the LOS channel capacity. The single input — single output (SISO) channel is described with the channel transfer function (CTF) h(f ). Solely considering the LOS signal part, the CTF is determined by the antenna displacement d0 and the speed of light. Presuming, that the transmission bandwidth B is much smaller than the centre frequency of the transmission channel fc, the frequency f can be approximated by fc. This is a well known, reasonable presumption in practical applications. h times left-parenthesi f right-parenthesi times almost-equals h times left-parenthesi f Subscript c Baseline right-parenthesi times equals times StartFraction up er C 0 Over 4 pi tmes period times d 0 times period f Subscript c Baseline EndFraction times period times e Superscript negative j times period times 2 times pi tmes StartFraction d 0 times period times f Super Subscript c Superscript Over c 0 EndFraction

Applying the plane wave model to the MIMO case, the propagation distances dmn between the n-th transmit antenna and the m-th receive antenna according to figure 1 is approximated by dmn = d0 + (m − 1) · dR · sin(αR) − (n − 1) · dT · sin(αT)· The CTF for an arbitrary Tx-Rx antenna pair can therefore be delineated hSubscriptmtimesnBaselinetimesequalstimesStartFractionup erC0Over4pitmesperiod 0timesperiodfSubscriptcBaselineEndFractiontimesperiodtimeseSuperscriptminusjBaseline.2piStartFractiondSuperSubscriptmtimesnSuperscriptperiodfSuperSubscriptcSuperscriptSuperSubscriptSuperscriptOverc0EndFractionBaselinetimesequalstimesStartAbsoluteValuehEndAbsoluteValueperiodtimeseSuperscriptnegativejtimesperiodtimes2piStartFractionfSuperSubscriptcSuperscriptSuperSubscriptSuperscriptOverc0EndFractiontimesperiodtimesleft-bracketd0timesplustimesleft-parenthesi mminus1right-parenthesi timesperiodtimesdSuperSubscriptup erRSuperscript imesperiodtimes inel ft-parenthesi alphaSuperSubscriptup erRSuperscriptright-parenthesi timesminusleft-parenthesi nminus1right-parenthesi timesperiodtimesdSuperSubscriptup erTSuperscript imesperiodtimes inel ft-parenthesi alphaSuperSubscriptup erTSuperscriptright-parenthesi right-bracketBaselinetimesperiod

The slight variation in channel path loss coinciding with the varying distances dmn is neglected by introducing the path loss |h|. StartAbsoluteValue h EndAbsoluteValue almost-equals StartAbsoluteValue h Subscript m n Baseline EndAbsoluteValue almost-equals StartFraction c 0 Over 4 pi times period times d 0 times period f Subscript c Baseline EndFraction times for-al left-brace m comma n right-brace

This is common practice for a small antenna spacing dT, dRcompared to the antenna distance do0 The MIMO channel transfer matrix H contains the CTFs between all results from any possible Tx-Rx combinations. Here an arbitrary entry m different entry hhn according to h Subscript left-parenthesi m plus times k right-parenthesi left-parenthesi n plus times l right-parenthesi Baseline times equals times h Subscript m n Baseline times period times times e Superscript negative j times .2 pi StartFraction period f Super Subscript c Superscript Over c 0 EndFraction Baseline times period left-bracket k times period times d Subscript up er R Baseline times period times ine times left-parenthesi alpha Subscript up er R Baseline right-parenthesi minus l times period times d Subscript up er T Baseline times period times ine left-parenthesi alpha Subscript up er T Baseline right-parenthesi right-bracket

with −m + 1 ≤ k ≤ M − m and −n + 1 ≤ l ≤ N − n

Figure 1. Spherical and plane wave model

This particularly means that all rows (l = const.) and all columns (k = const.) of the CTM H are linearly dependent. Thus, the rank of H is rank {H}= 1 and it follows HHH |h|2 • N •1M×M =

where 1 denotes the matrix consisting of all entries [1]ij = 1. The channel capacity of such a MIMO channel transfer matrix reduces to its minimum: up er C Subscript min Baseline times equals times log Subscript 2 Baseline times left-parenthesi 1 times plus times StartFraction sigma Subscript x Superscript 2 Baseline Over sigma Subscript eta Superscript 2 Baseline EndFraction times period times StartAbsoluteValue h EndAbsoluteValue squared period times up er M times period times up er N right-parenthesi

Hence, the application of the plane wave model results strictly in a CTM with rank one and a channel with minimum capacity. In the opposite case, the maximum capacity is achieved by a CTM with optimum eigenvalue profile. The upper limit for the channel capacity is given by2 up er C Subscript max Baseline times equals times min times StartSet up er M comma up er N EndSet period times log Subscript 2 Baseline times left-parenthesis 1 times plus times StartFraction sigma Subscript x Superscript 2 Baseline Over sigma Subscript eta Superscript 2 Baseline EndFraction times period times StartAbsoluteValue h EndAbsoluteValue squared period times times max times StartSet up er M comma up er N EndSet right-parenthesis times period

If the spherical wave model is applied, every entry hmn of the CTM H must be delineated in its very general form h Subscript m n Baseline times equals times StartFraction up er C 0 Over 4 pi times period times f Subscript c Baseline EndFraction times period times left-bracket StartFraction 1 Over d Subscript m n Baseline EndFraction times period times e Superscript minus j Baseline .2 pi StartFraction d Super Subscript m n Superscript imes period f Super Subscript c Superscript Super Subscript Superscript Over c 0 EndFraction Baseline right-bracket for-al m times element-of StartSet 1 times el ipsis up er M EndSet comma n times element-of StartSet 1 times el ipsis up er N EndSet period

The most important consequence is now, that by optimizing the antenna distances, it is possible to construct high rank CTMs leading to high capacity LOS MIMO channels, as it is shown in the following subsection. In [9] the authors suggest a threshold distance dth, which indicates the mandatory usage of the spherical wave model for shorter distances than dth. The threshold distance marks the distance d0 where the error caused by the plane wave assumption results in a capacity error of 50%. The given formula d Subscript h Baseline times equals times left-parenthesi 4 times period times left-parenthesi times up er M minus 1 right-parenthesi times StartFraction d Subscript up er R Baseline times period f Subscript c Baseline Over c 0 EndFraction times period times left-parenthesi up er N minus 1 right-parenthesi times StartFraction d Subscript up er T Baseline times period times f Subscript c Baseline Over c 0 EndFraction right-parenthesi times period StartFraction c 0 Over f Subscript c Baseline EndFraction

delivers e.g. for a 4 × 4 WLAN application at fc = 2.4GHz and a small antenna 1.13m. This result suggests spacing of half-wavelength at Tx and Rx a value of dth the usage of the plane wave model for most indoor applications, resulting in a rank deficient CTM and a low MIMO capacity. This conclusion is revealed to be fatal if a larger antenna spacing is considered. Assuming a spacing of dT = dR = 3λ =

together with similar system parameters, the threshold increases to dth =40.67m, which indicates the necessity of the spherical wave model for almost any indoor scenario.

2 Note again, that m is the transmit power allocated to each transmit antenna.

4.2. LOS Optimised Antenna Setups The capacity of a MIMO channel depends on its eigenvalue profile which is influenced by the antenna distances dmn in a LOS MIMO channel. Hence, it is obvious that the LOS channel capacity is increased by optimizing the antenna setup. Here, the phase angle relations between the entries of the CTM are considered and varied until the CTM has an optimum eigenvalue profile. After several proposals for a limited number of antennas, the authors in [11] delivered a prescript for the geometrical antenna arrangement in order to achieve capacities close to the maximum. An M × N MIMO system endowed with uniform linear arrays (ULAs) is considered. It is shown that an optimum LOS antenna arrangement is found if the antenna separation product ASP(κ) = dT · dR fulfils the following condition: normal upper A upper S upper P times left-parenthesis kappa right-parenthesis times equals times StartFraction lamda dot d 0 dot kappa Over upper V dot cosine times theta Subscript upper R Baseline dot cosine theta Subscript upper T Baseline EndFraction comma kappa element-of left-brace n element-of double-struck upper N times colon n times indivisible by upper V right-brace comma upper V colon equals times max times StartSet upper M comma upper N EndSet

Figure 2 illustrates the antenna arrangement. Although this solution is based on some slight simplifications, very accurate simulation results are reported. Independently, this result is also presented in [12] where the authors further prove the theory on LOS channels using 2 ×2MIMO measurements in an anechoic chamber. The theoretical and the measured capacities in the absence of NLOS signal parts agreed very well. For the further analysis of the LOS MIMO channel two different antenna setups consisting of ULAs are considered. The first antenna setup is characterised by broadside ULAs and delivers a high capacity which can be optimised close to the maximum by choosing all distances according to [ 11 ]. In the opposite, the perpendicular setup of two ULAs is found to provide a channel capacity close to the keyhole case. If the analysis is limited to ULA antenna arrangements, these setups deliver an upper and a lower limit for the channel capacity. Of course the ULA is not the optimal antenna setup for MIMO systems, but it is exemplarily used here to demonstrate the antenna setups influence on the channel capacity. The simulation

Figure 2. MIMO system with ULAs and the ULA setups broadside and perpendicular

Figure 3. Capacity simulation results for different antenna spacing including the path loss

results presented in figure 3 prove the theoretical analysis. The antenna setup that was exemplarily optimised for a Tx-Rx distance of 3m achieves maximum capacity at d0 = 3m. The capacity remains quite high for small variations of d0 around the optimum and decreases for larger Tx-Rx displacements. For shorter displacements high capacity is achieved compared to the theoretical maximum. The obtainable capacity is close to its minimum if a setup with an antenna spacing of λ/2 is chosen. Channels Multipath LOS Indoor Real-World of Capacity 5.

The previous section outlined the pure LOS channel in the absence of any NLOS signal parts. It was shown to be possible to construct antenna setups leading to an optimum eigenvalue profile as well as setups that provide rank deficient channels. In real world scenarios the influence of the NLOS signal parts on the capacity of such channels has to be considered as well. The LOS and NLOS signal components interfere with each other at the receiver, disturbing the constructed phase angle relations. NLOS signal parts consist of reflected, scattered or diffracted waves that impinge with a delay at the receiver. In order to determine the influence of the NLOS parts on the channel capacity, measurement campaigns with LOS optimised antenna setups were carried out. The results presented in figure 4 and 5 are taken from measurements at 2.4GHz and represent exemplary results taken from a large measurement database. For a more detailed description of the measurement

Figure 4. Theoretical and measured capacities for different antenna setups as well as the measured scenarios the reader is referred to [ 13 ] and the references therein. The measured channel capacity in different scenarios is compared with theoretical results for the pure LOS channel and the limits for the LOS capacity in figure 4. It can be figured out, that the NLOS signal parts that are present in the measurement scenarios are not harmful to the capacity of LOS optimised channels. For channels with reduced LOS capacity, in the opposite case, they are

equipment

beneficial. Here, the NLOS signal parts are capable to improve the pure LOS Even weak MPCs, as they occur in large halls with no scattering objects close to the antennas, are capable to increase the low LOS capacity of suboptimal antenna setups. Strong sparse MPCs from favourable directions help to increase the capacity up to the maximum. When analysing the influence of NLOS signal parts on the channel capacity, the angles of arrival (AOA) of the MPCs have to be considered. An AOA of 0° even

capacity.

describes a signal component that impinges perpendicular to the ULA, while an AOA of 90° is defined for a signal component arriving parallel to the ULA. It has been determined in [ 13] that signal parts with an AOA around 0° help to increase the channel capacity by forming a better eigenvalue profile, while for an angle around 90° their influence on the channel capacity is negligible and only measurable because of the increased receive power. The conclusion that the NLOS signal parts are beneficial for the capacity of suboptimal LOS channels holds true, only if they impinge from favourable direction. A higher number of measurement results has to be evaluated for a more general statement about the capacity of the indoor LOS channel. As the channel can be treated as time invariant for short durations, it seems reasonable to create a spatial statistic over a certain area of interest. Here, the antenna positions for Tx and Rx are treated as random values inside the investigated area which might be a room or hall. a

The cumulative distribution functions (CDFs) in figure 5 depict measured capacities in a typical large office scenario at 2.4 GHz. The Tx-Rx displacement was kept constant at 3m, while the antenna spacing of the used ULAs was

Figure 5. Capacity CDFs for indoor LOS multipath channels at m in a typical office scenario

= 107

varied. With broadside ULAs a generally high capacity is obtained for both cases (2 × 2 and 4 × 4). This becomes obvious if the results are compared to the theoretical maximum for the LOS channel capacity, which is 15.2Bit for the 2 × 2 case and 34.4Bit for the 4 × 4 case. The high measured capacities prove that NLOS signal components have no negative influence on the capacity of MIMO channels. Due to the increased receive power the measured capacity is even higher than the theoretical LOS capacity. Regarding the perpendicular ULA arrangement, it turns out that the capacity is reduced to about 85% of the optimum case, but it is still much higher than in the theoretical pure LOS case. It can be concluded that for every measured antenna position NLOS signal parts from beneficial directions arrived at the receiver increasing the low pure LOS capacity. This is an important result, as it is not possible to optimise the antenna setup with respect to the LOS signal in every application. As another key result it turns out that an antenna spacing of half-wavelength is insufficient to achieve adequate MIMO channel capacities. The measurement results for the capacity of this antenna spacing are even lower than those for the worst case with larger antenna spacing. Hence, the antenna spacing has to be chosen distinctly larger than half-wavelength in order to achieve high MIMO capacities in correlated channels.

6. Exemplary Link Level Analysis It is well known that the Shannon channel capacity only marks a theoretical upper bound for the capacity or data rate which can be achieved in a particular channel. Unfortunately, in practical systems the achievable performance not necessarily reaches this theoretic bound due to degradations caused by practical transmission and detection techniques. However, independently from the particular MIMO

detector the orthogonal LOS MIMO channel results in a much lower bit error rate (BER) than its suboptimal counterpart [14]. To show this, in the next paragraph the BER for a 2 × 2-MIMO system for two different channels is exemplarily investigated in order to study the channel from a link level perspective. Of course the benefit in form of reduced BER strongly depends on the chosen detector. The MLdetector is of particular interest, as it is known to be the optimal receiver for MIMO systems [15] although it can hardly be practically implemented because of its high complexity. The focus of the following is to show the impact of the MIMO channel on the BER, but not to discuss any particular detection scheme or its complexity. Thus, we apply the ML detector as the optimum detector, although it can not be practically implemented. For the simulation we assume temporally uncoded transmit symbols which are equally probable using 64 QAM. Furthermore, the receiver is assumed to have perfect channel knowledge. We exemplarily compare two different channels which differ in their channel eigenvalue profile (CEP) and are denoted as follows: StartLayout EndLayout StartLayout 1st Row 1st Column optimal CEP left-parenthesis orthogonal chan el right-parenthesis 2nd Column suboptimal CEP 2nd Row 1st Column up er H Subscript normal o normal p t imes equals Baseline times StartFraction 1 Over StartRo t 2 EndRo t EndFraction Start 2 By 2 Matrix 1st Row 1st Column 1 2nd Column 1 2nd Row 1st Column 1 2nd Column negative 1 EndMatrix 2nd Column up er H Subscript s times minus normal o normal p t equals Baseline times Start 2 By 2 Matrix 1st Row 1st Column 0.2898 minus 0.2094 j 2nd Column 0.7691 minus 0.2 96 j 2nd Row 1st Column negative 0.5354 minus 0.0496 j 2nd Column negative 0.1652 minus 0.9837 j EndMatrix EndLayout

Employing these channel realizations the channel capacity is calculated according to C

=

log2 [det (IM + SNRRx • H

•

HH)]

where H is either set Hopt or Hs_opt. As it is observed from figure 6 the channel capacities of the both channels differ around 15% which ranges in the order of magnitude of the measured capacity differences in section 5. A comparison of the Frobenius-norm, which is the sum of the squared matrix entries and, therefore, indicates the power, shows a ratio of m This means, that the path loss in both channels is almost identical which also agrees with the measurements. Thus, the both channels represent the measurements very well. Proceeding to the BER results depicted in figure 7 it can be clearly observed that the optimal-CEP channel outperforms the suboptimal-CEP channel. Taking for example a BER of 10-3 the SNR-gain of the orthogonal channel is about 6.25dB. Although the capacity difference is only about 15% a very reasonable SNR-gain in the BER performance is obtained. Keeping in mind that the ML is the optimum detector, it can be expected that suboptimal detectors like the zero-forcing approach, which distinctly suffers from channel correlations, will exhibit an even ,

.

,

performance. light of the results from the exemplary link level analysis, the effort of optimizing the antenna setups at Rx and Tx in order to construct orthogonal MIMO channels is further justified.

worse

In the

Figure 6. Capacity of simulated MIMO channels

Figure 7. Uncoded BER of simulated MIMO channels (ML equalizer 64 QAM)

7. Conclusion The capacity of indoor LOS MIMO channels has been analysed. Figuring out the influence of the geometrical antenna setup, it is shown that the capacity of LOS channels is significantly increased by optimising the antenna setup. The commonly used half-wavelength antenna spacing at Tx or Rx is definitely insufficient in order to achieve high MIMO capacities. Especially for the upcoming WLAN standard IEEE 802.1 In this is an important fact, as already many hardware components with too small antenna spacing exist, exhibiting a data rate performance which is far below the expectations. Contrarily to the SISO case, the antenna setup has a tremendously large influence on the channel characteristics of MIMO systems. Thus, it is definitely required to regard the antennas when modelling the indoor LOS channel [ 5 ] as the channel model itself is the basis for any development of system components. Taking for example the equalizer, which is commonly designed using a Rayleigh fading channel, it was shown that large performance discrepancies occur for different LOS channels, although the corresponding capacity discrepancy might be small.

Acknowledgements The authors would like to thank their colleagues M. Chouayakh and Prof. B. Lankl for their scientific support and many helpful discussions. Furthermore, the authors would like to thank D. Ogermann and R.T. Schwarz for their assistance with the MIMO measurement campaigns. Finally, the authors express their thanks to Dr. I. Sarris for providing useful comments on their work.

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Capacity of multi-antenna Gaussian channels ”, AT&T-BeU Techn. Memorandum 1995 On the limits of wireless communications in a fading environment when using multiple antennas ”, Wireless Personal Communication vol. 6 pp. 311 335 1998 P. W. Wolniansky G. J. Foschini G. D. Golden and R. A. Valenzuela V-BLAST: An architecture for realizing very high data rates over the rich-scattering wireless channel ”, in Proceedings URSI International Symposium on Signals, Systems and Electronics ( IEEE New York, NY, USA ), E. Telatar

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Design of Compact Antenna Arrays for MIMO Wireless Communications Yuanyuan Feia, 1 and John Thompsona a Institute for Digital Communications, University of Edinburgh, Kings Buildings, Edinburgh, United Kingdom. Abstract. Theoretical analysis and measurements have indicated that closely spaced or compact antenna arrays (typically smaller than half the carrier wavelength) can achieve good performance in multiple input multiple output (MIMO) wireless communications. This is an important result which could lead to MIMO technology being deployed even on small wireless terminals. However, these results need to take into account the effect of mutual coupling which arises between closely spaced antenna elements. In this chapter, we discuss how mutual coupling can be properly modeled in a MIMO wireless system. We also discuss how simple matching networks that take into account the mutual coupling effect can be used to provide significant performance improvements in compact antenna array receivers. We provide simulation results for a 2 × 2 MIMO system to verify the effect of different matching networks and show results for the sensitivity of MIMO performance to errors in the matching network components and antenna element dimensions. Our results show that optimizing a single-port matching impedance is a simple but promising approach to improve the performance of compact arrays. Keywords: Wireless Telecommunications, 4G, Multiple Input Multiple Output (MIMO), mutual coupling, matching networks, sensitivity analysis.

1. Introduction The study of compact arrays in small wireless receivers has recently received significant attention from researchers. In narrowband multiple input multiple output (MIMO) systems, it is widely agreed that the mutual coupling (MC) effect, which arises between closely spaced antenna elements in an antenna array, can reduce the signal correlation by distorting the radiation patterns of each element [1,2,3]. However, it will also induce a mismatch between the characteristic impedance of the circuit and the antenna input, which is detrimental to the received signal power level [4]. These conflicting results from the MC effect are one important factor which contributes to differing conclusions concerning its impact on MIMO capacity performance. Some work claims that MC is a benefit to MIMO systems [3,5,6],

1 Corresponding Author: Yuanyuan Fei, Institute for Digital Communications, School of Engineering and Electronics, University of Edinburgh, Kings Buildings, Edinburgh, EH9 3JL, UK. Email: [email protected]

DOI: 10.1201/9781003336853-24

Design of Compact Antenna Arrays for MIMO Wireless Communications

some completely disagree with the first claim [7,8,9], while a third group [2,4,10,11] believe that the MC only leads to performance advantages in certain specific cases, e.g. a selected range of antenna spacings. This divergence of opinion is caused by different channel normalization criteria, various power allocation strategies at the transmitter and whether the effect of the receiver matching network is under consideration. Within these studies, only [2,6] included the matching network of the receiver in their MIMO system evaluations. Two methods in n-port theory are usually adopted to study compact MIMO systems. One is S-parameter analysis which reflects the wave transmission in an n-port electrical network; the other is Z-parameter analysis which expresses the voltage and current relations among all ports. The S-parameter framework has been examined in detail in [2 ], and recently improved by analysing the effect of amplifier networks on the coupled receiver [ 12]. The authors of [2 ] introduce several matching networks to improve the system performance, while other types of antenna matching networks are examined in [6 ]. It is proved in [2 ] that the so-called multiport-conjugate match can realize zero output correlation and lossless power transfer from the antennas to the loads for any antenna spacing, thus offering significant capacity improvement for very small antenna spacings. However, it turns out that the optimum multiport-conjugate match can only be achieved for a small system bandwidth [ 13], which is in contrast to the desire to use large system bandwidths in future broadband wdreless communication networks. Apart from this issue, the multiport-conjugate match is not easily implemented in practice as it requires multiple circuit components to be interconnected across the antenna ports. Instead, the single-port match [4 6 13] is a practical, if suboptimal solution, as it provides capacity improvement compared to the non-matched case and has a much broader bandwidth than the multiport-conjugate match. The impact of the single-port match on the performance of MIMO systems can be studied using a Z-parameter approach, and this evaluation has been partially ,

,

been carried out in [4 7 10 14 15]. In [4 14] the authors focus on the 2 x 2 MIMO system. The optimal single-port matching impedance for capacity maximization is first observed in [ 14] for certain antenna spacings, and then more antenna spacings are investigated in [4 ]. We have proved in [ 16] that the optimal single-port matching ,

,

,

,

,

impedance for capacity maximization can be found analytically for any antenna spacing. Initial results for the study of matching with larger array sizes in compact MIMO systems can be found in [ 17]. However, the system sensitivity of the 2 x 2 MIMO system has not received a lot of attention as the capacity performance relies on the practical design of the compact receiver [ 15 ]. The importance of matching networks in compact array and their sensitivity to small parameter changes will be discussed in detail in this chapter. The remainder of this chapter is organized as follows. Part 2 describes the system model and how the effect of mutual coupling and receiver matching networks can be included into the performance evaluation of MIMO systems using Z-parameters. Part 3 presents simulation results which investigate the performance and sensitivity of different coupling techniques on MIMO performance. Finally, Part 4 presents our conclusions.

2. MIMO System Model

2. MIMO System Model A MIMO system with N transmit and N receive antennas is considered in this chapter. For simplicity it is assumed that the channel is frequency-flat fading, and the total average energy at the transmitter over one symbol period is P. The inputoutput relation for a symbol period is: normal y times equals times StartRoot upper P slash upper N EndRoot normal upper H normal x times plus times normal v

where y =[y1,... yN]T is the received signal vector and x =[x1,...,xN]T is the transmitted signal vector. H represents the MIMO channel with dimension N × N, and the additive Gaussian noise vector is v =[v1,...,vN]T with covariance matrix E[vvH]= N0I. The superscripts T and H means transpose and conjugate transpose, while E[·] denotes the expectation operator. Finally, I is an N × N identity matrix. 2.1. Capacity of MIMO Channels We assume that H has no preferred transmit direction, and is perfectly known at the receiver. This implies the optimum transmit signals to maximize capacity are independent and equal-power waveforms at the transmit antennas [18]. The narrowband MIMO Shannon capacity is given by: C

=

log2

det

[I + (ρ/N)HHH]

where ρ is the signal-to-noise (SNR) ratio. Moreover, we assume the channel has rich-scattering at both ends, as well as the transmitter antennas being located far apart. Then the channel H can be expressed by the semicorrelated Kronecker model [19]: H = R1/2Hiid If the uniformly distributed arriving signal model in space is assumed, the receive 1 and Rii= J0(2πd/λ) [20 ], where J0() end correlation matrix R has elements Rii and d, and are the zero order Bessel function and the receiver antenna spacing. The matrix Hiid is an N x N independent and identically Rayleigh distributed (i.i.d.) channel matrix. =

2.2. Effect of Mutual Coupling As compact receive antennas are considered with spacings d < 0.5λ, the MC effect becomes an important one to model properly. MC can be explained as an interaction caused by neighboring elements inducing extra voltages between each other. In port theory, the mutual impedance matrix Z is defined as normalup erZtimesequalstimesStart3By3Matrix1stRow1stColumnup erZ1 2ndColumnup erZ123rdColumn elipsi 2ndRow1stColumnup erZ212ndColumnup erZ2 3rdColumn elipsi 3rdRow1stColumn elipsi 2ndColumn elipsi 3rdColumn elipsi EndMatrix

Figure 1. Block diagram of the coupled MIMO receivers with matching networks

where

means the mutualZii is the self-impedance of the ith element and impedance between the ith and jth elements. Here the equality Zij Zji is based on the reciprocity theorem [21 ]. In Figure 1 the matching-impedance matrix ZL is a diagonal matrix whose ith diagonal entry is ZLi which is the matching impedance in the ith antenna branch. Assuming there is no MC between the matching impedances, the non-diagonal elements of ZL are zero. In this chapter, the antenna elements are Zij

=

,

considered identical and the load elements are assumed to be identical too, so that the diagonal entries of ZL are all equal to ZL. By utilizing the voltage-current relations [22 ], the MC coefficient matrix is:

Ωmc

=

(Z

+

ZL)-1

=

(Z

+ Z

I)-1

2.3. MIMO Capacity with Mutual Coupling The MC effect at the receiver can be easily included into the MIMO model [ 11 ] Ωmc H where Hmc is the modified MIMO channel by using the relation Hmc with MC. Suppose that the matching networks are perfectly lossless and the each transmitter has the self-conjugate Z11* match (* denotes the complex conjugate). Without the MC effect, the MIMO system will always have an antenna power gain of (4R11RL) when normalized to the self-conjugate matched single antenna case 14 2 x 2 system, a point which should be included in the system evaluation. for a [ ] and RL are the resistances (real parts) of Z11 and ZL, respectively. The modified R11 MIMO capacity expression is thus: =

Cm

=

log2 det

[I + (ρrR11RL/N)HmcHHmc]

where ρr is the reference SNR of the system which clearly depends on N0. An identical result has been derived in [4], though obtained from a different perspective. Now define the ergodic capacity of the MIMO link as E[Cm]. Using Jensen’s inequality and the concavity of the log det function [23], we can take the expectation inside the log det function and obtain an upper bound Cup at each impedance matching load point ZL0 as:

Cup

=

log2 det

[I + (ρrR11RL0/N)ΩR] ≥ E[Cm]

where RL0 is the real part of ZL0. As we will see in Section III, Cup is very helpful for simplifying the evaluation of the optimum impedance match and for measuring the sensitivity of MIMO capacity to impedance match imperfections.

3. Simulation and Analysis To illustrate the

impact of MC on MIMO systems, a basic 2 x 2 system configuration

is simulated under the conditions presented in Part 2. Identical ideal half-wavelength dipoles with infinite thin wire diameter are used at both ends since they often taken as references in the antenna field. Now we focus on the coupled receive end. Under this ideal assumption, the self-impedance Z11 73 + j42.5 ohms is constant, and the mutual-impedance Z12 Z21 is calculated using the modified EMF method [22 ]. For each load point ZL0, 10000 random channel realizations are deployed to =

=

estimate the MIMO system performance with ρr

=

15dB.

3.1. Capacity of Different Impedance Matching Techniques As shown in Figure 2 the 3-dimensional ergodic capacity surface is plotted with various matched impedances points ZL0 = RL0 + jXL0. We take the d 0.05λ case as an example to demonstrate that the capacity performance is concave and as in [14] one peak is observed with the changing of matching networks at one fixed value of d. For other antenna spacings less than 0.5λ, the surface of Cm has the similar ,

=

properties. Although

the multiport-conjuate match is theoretically attractive to improve the compact array performance in MIMO systems [2], it is difficult to implement in practice given the current state of the art. Therefore, the optimum single-port impedance match, which gives the best MIMO performance for specific antenna spacing, should be investigated as a simpler alternative. Figure 3( a) plots the optimal matching impedances Zopm (i.e. the peak co-ordinate of Figure 2 ) vs the antenna spacing d (< 0.5λ for compact arrays) for both the mean and upper bound capacities of the system. It is clear that the simulation results agree very well as each dot (Cm)

Figure 2. Ergodic capacity vs. the real and imaginary parts of ZL for d = 0.05λ

Figure 3. (a) The optimal matching impedances Zopm = Ropm + jXopm versus antenna spacing for the mean capacity and upper bound capacity of the system (b) The mean capacity (solid line) and upper bound capacity (dash line) with various matching networks vs antenna spacing (SNR = 15dB) is almost in the centre of the circle (Cup) it corresponds to. This means we can use the capacity upper bound in place of the actual capacity result to determine the optimum impedance match very simply. To show how much we can benefit from the Zopm matching, the mean capacity and upper bound capacity have been computed for ideal antennas with characteristic-impedance match both with no coupling (Z0nc) and with MC (Z0), the self-conjugate match (Z11*), and the Zopm match. The results for these comparisons are shown in Figure 3(b) The coupled compact array with matching networks outperforms the array without MC at small .

spacings (d < 0.2λ). Meanwhile, the Zopm match surpasses other matching schemes when d < 0.25λ. Another interesting phenomenon is the slope of the results for Cm and Cup are nearly the same for different matching pairs with d > 0.15λ, which is very useful for investigating the sensitivity of MIMO capacity results. We look back to Figure 2. Despite of the superiority of Zopm match, we need to consider how its sensitivity to small changes in receiver configuration will impact practical implementation. 3.2. Capacity Sensitivity Results The sensitivity of the matching network is important as it will vary with the environment (temperature, humidity, etc.) as well as due to design accuracy limitations. We define the performance efficiency of Cm for given d and matching impedance ZL0 as: etaSubscriptmBaselinetimesleft-parenthesi up erZSubscriptup erL0Baselineright-parenthesi tmesequalstimesStarFactionup erCSubscriptmBaselinel ft-parenthesi up erZSubscriptup erL0Baselineright-parenthesi Overmaxleft-bracketup erCSubscriptmBaselinel ft-parenthesi up erZright-parenthesi right-bracketEndFractiontimesequalstimesStarFactionup erCSubscriptmBaselinel ft-parenthesi up erZSubscriptup erL0Baselinetimesright-parenthesi Overup erCSubscriptmBaselinel ft-parenthesi up erZSubscriptopmBaselinetimesright-parenthesi EndFraction

The notation Cm(ZL0) emphasizes the dependence of Cm on the matching impedance ZL0. The specified precision error of the resistive and reactive components, ΔR and ΔX, relative to the optimum values in Zopm for the matching 2 implies a component error of impedance, are normalized to 50 ohms, so ΔR 100 ohms in RL. It should be clear that Zopm defines the origin in a plot of ΔR —

Figure 4, Upper bound capacity efficiency contours for ηup 0.9, 0.95 and 0.99 as a function of ΔR and ΔX with (a)d 0.15λ. Special matching impedances Zopm (dots), Z0 0.05λ and (b) d (triangles), and Z11* (squares) are also marked (SNR 15dB) =

=

=

=

and

ΔX. We assume that the

matching networks of both receivers have the same precision simultaneously. The scalar ηup is defined in the same way for Cup and it turns out [15] that the load impedance that maximizes Cm also approximately maximizes Cup. Therefore ηup is used to generate results for the capacity sensitivity, error

which avoids the extensive Monte Carlo simulations needed to evaluate ηm. Figure 4 gives us a clear demonstration of the deterioration in MIMO performance due to mismatches in the optimal impedance for two different antenna spacings. For example, Figure 4(a) tells us that the system capacity reduces by 1% if the normalized error ΔR exceeds the range [—0.13, +0.3] or ΔX exceeds ±0.09. The results also show that Z0 and Z11* matching impedances achieve around 95% of the maximum system capacity, as would be expected from Figure 3(b) Increasing 0.05 to 0.15λ. significantly increases the 99% and the antenna spacing from d 95% capacity regions in Figure 4(b) suggesting that the matching is somewhat less .

=

,

sensitive for larger antenna spacings. In addition, the Zopm and Z11* matches are closer in value, again following the convergence of these two matching approaches as d increases in Figure 3(b) Even for d 0.05λ the MIMO capacity is not very sensitive to small errors in the matching values ΔR and ΔX. .

=

Besides antenna spacing and matching networks, the accuracy of the antenna dimension is another factor which can degrade MIMO performance due to changes in the self and mutual impedances. The impedance values are simulated based on the approach in [24]. Figure 5(a) shows that for d = 0.05λ the performance of the Zopm match is very sensitive to small errors in the antenna length. However Figure 5(b) shows that the Zopm match does not degrade so quickly for d = 0.5λ. The highest capacity of the Z0 match is attained for an antenna length of 0.486 λ, which is the first resonant length Z11 = R11 of a dipole antenna. Figure 5 also shows that the Z11* match gives the most stable performance of the three methods. The results demonstrate that MIMO capacity is not sensitive to antenna length at all for this form of matching. Therefore, the Z11* match is probably the best matching network when the dipole length is not precisely known.

Figure 5. The mean capacity (dash line) and upper bound capacity (solid line) with various matching networks for (a) d = 0.05λ and (b) d = 0.15λ. (SNR = 15dB)

4. Conclusion The performance sensitivity of a 2 × 2 MIMO system with coupled half-wavelength dipoles and decoupling matching networks is presented in this paper. By utilizing MIMO capacity results and upper bounds which include the mutual coupling and matching networks effect, the optimal single-port matching impedances for various antenna spacings can be found from analysis or simulation. Optimum matching outperforms other matching networks, particularly for small antenna spacing (d < 0.25λ). When antenna spacing and dipole lengths are fixed, the MIMO capacity is not particularly sensitive to small mismatches in the optimal impedance. However, the optimal matching network is relatively sensitive to small changes in antenna size. Despite this limitation, the optimal single-port match is a simple and effective technique to improve the performance of MIMO systems using compact antenna array receivers. Recent work has also derived analytic techniques [16] to determine the optimum impedance value, simplifying the calculations required.

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Space-Time Error Correcting Codes and Iterative Decoding Massinissa Lalam 1, Karine Amis and Dominique Leroux GET - ENST Bretagne, Brest, France Abstract. The space-time error correcting codes(STECCs) are an efficient new space-time block code family built from any linear forward error correcting code (FEC) for two transmitThe key principle is the FEC linearity which is exploited to transmit linear combinations of FEG codewords to create a space-time redundancy. However, the bottleneck of these codes

ters.

is the detection whose

complexity

grows

exponentially with

the number of FEC codewords

involved in the creation of one STECC codeword. By applying turbo equalisation and adapting it to the STECC structure, we can significantly reduce this complexity, while achieving an

equivalent

level of performance.

Keywords: Multiple-Input Multiple-Output, Space-Time Coding, FEC, Iterative Decoding, Turbo Equalisation.

1. Introduction The demand for high-quality and high-data rate wireless services has kept on growing for the past few years, while the spectral bandwidths are scarce and the transmission power limited. It is difficult to achieve simultaneously high transmission quality and high information data rate in a band-limited wireless context as the available throughput is upper-bounded by the channel capacity defined by Shannon in his famous paper [ 1 ]. Since the mid 90’s multiple-input multiple-output (MIMO) systems have been intensively studied as a way to increase the transmission quality and/or useful data rate. Two families of MIMO coding schemes have been essentially developed in literature: MIMO coding schemes based on block and MIMO coding schemes based on trellis. The MIMO coding schemes based on block can be sorted into two groups. The first group deals with the transmission quality by exploiting the space-time diversity. It is mainly composed of the space-time block codes (STBCs) and especially orthogonal ones (OSTBCs), as introduced by Alamouti [2 ] and generalized by Tarokh et al. [ 3]. They offer good performance but a poor spectral efficiency when the number of transmit antennas becomes larger than two. The second gro up increases the transmission throughput and takes advantage of the multiplexing gain. It is mainly

1 Massinissa Lalam, GET-ENST Bretagne, TAMCIC (UMR 2872 CNRS), Département Signal & Communications, Technopôle Brest Iroise CS 83818 - 29238 Brest Cedex 3, France. Email: [email protected]

DOI: 10.1201/9781003336853-25

Space-Time Error Correcting Codes and Iterative Decoding

composed of the layered space-time (LST) architectures [4 ]-[ 6], which are close to a spatial multiplexing of the modulation symbols. The golden codes [7 ] and the TAST codes [8 ] are full-rate and full-diversity and thus can achieve high spectral efficiencies. Their optimal detection is more difficult, but can be significantly reduced against the overall transmission quality by using sub-optimal techniques such as sphere decoding [9 ], zero forcing (ZF) or minimum mean square error (MMSE) filtering. However, these MIMO coding schemes do not possess error correction capability. Therefore, forward error correcting codes (FECs) are added to guarantee a given transmission quality level. The most common one is the space-time bit interleaved coded modulation (ST-BICM) [ 10]. On the contrary, the MIMO coding schemes based on trellis, named space-time trellis codes (STTCs) [ 11 ], include FEC techniques in their design and make use of the Viterbi algorithm [ 12] for their decoding. They exhibit good performance but their decoding complexity is always an exponential of the modulation order. This complexity can be slightly reduced at the expense of a spectral efficiency reduction with the introduction of orthogonal properties [ 13], [ 14]. The space-time error correcting codes (STECCs) we developed are space-time block codes for two transmit antennas that also include an error protection at the centre of their design. They are built on any linear FEC. The first antenna transmits K FEC codewords and the second one linear combinations of these K FEC codewords, creating a space-time redundancy. The receiver exploits the particular space-time structure as well as the FEC linearity to estimate the transmitted information bits. While the STECC achieves a good compromise between high information throughput and reliable transmission, its detection complexity grows exponentially with the parameter K.

Since the introduction of the turbo codes [15], [16] in the 90’s, many promising applications of the turbo principle were done, especially in the equalisation domain [17]. Application of this technique in the STECC decoding [18] allows a significant complexity reduction which cannot be obtained in the STTC case. In this paper, we present the use of the turbo equalisation in the STECC decoding to decrease the decoding complexity without degrading the performance. Section 2 describes the STECCs and the turbo equalisation. Section 3 presents the simulated performance obtained in the usual MIMO context. Section 4 discusses the previous results and highlights the performance of the STECC as well as the impact of iterative decoding while section 5 concludes the paper.

2. Material and Methods 2.1. The MIMO transmission model We assume a TDMA transmission model where each transmitted slot consists of τ modulation symbols. The channel state keeps constant over a slot and changes independently from a slot to another. The channel statistics are described by a Rayleigh

2. Material and Methods flat fading model. We assume perfect synchronisation and channel state information (CSI) at the receiver side. Therefore, the sampled receive signal is represented by:

r = Hs + n where

r

is the

×

nr

1 receive

m m

is the nt × 1 transmit signal with m channel matrix and n is the nr × 1 complex AWGN with

signal,

s

.

2.2. The Space-Time Error Correcting Codes A STECC is a space-time block code able to correct errors due to the transmission. Its key principle is the space-time redundancy created by using the FEC linearity. 2.2.1. Encoding Let C be a linear FEC of coding rate Rc and SC be the associated codeword set. We consider K FEC codewords from SC and an M-order binary to symbol conversion (BSC). For 1 ≤ i ≤ K, we denote: • •

ci one

of the K

original FEC codeword and si its modulation symbol version,

of the K combined FEC codeword and s≠i its modulation symbol version, where m stands for the addition in the set Sc (typically the addition modulus 2). one

m

The STECC is defined for nt = 2 transmit antennas and denoted d STECC codeword is given by the following matrix:

. One

m

where each row is sent through one antenna after BSC as shown in Figure 1. The STECC coding rate, defined as the number of useful information bits over the total number of bits, is independent from the parameter K and equals to: RSTECC = 0.5Rc

Figure 1. Transmitter scheme

2.2.2. Decoding We assume that the CSI is perfectly known by the receiver depicted in Figure 2. With equal power repartition between the transmit antennas and a unitary gain between each transmit and receive antenna, the signal to noise ratio (SNR) per receive antenna is given by: up er S up er N up er R times equals times m Subscript b Baseline times n Subscript Baseline times up er R Subscript up er S up er T up er E up er C up er C Baseline times StartFraction up er E Subscript b Baseline Over up er N 0 EndFraction Subscript Sub Superscript Baseline

where mb is the number of bits per modulation symbol, Eb the energy per useful bit and N0 the noise power spectral density. We denote si one modulation symbol of si and m one modulation symbol of m The K symbols m are totally defined by the K symbols si. Therefore, by finding the K symbols that maximize the likelihood, the STECC detection achieves an optimal detection with an MK complexity, which takes advantage of the spacetime diversity introduced and not only the space diversity as in a classical ML detection. This detection is called STECC detection and can easily produce log.

likelihood ratios for each detected bit.

After the detection stage, the decoding stage decodes the 2K FEC codewords. The decoding algorithm is supposed to be a soft-in soft-out (siso) algorithm that operates with LLRs. As the decoding is performed without taking into account the STECC structure, we add a combiner stage that exploits the STECC properties by computing new soft outputs from the decoded ones. For 1 ≤ i ≤ K, let: •

•

ci,j be the lth bit of the

original

FEC codeword ci and Λi,l

be its associated

LLR, c≠i,l be the lth bit of the combined FEC codeword c≠i and Λi,l ciated LLR.

be its

asso-

For simplicity, we omit the index l in the rest of the paper. The updated LLR associated to the bit ci conditionally to the previous LLRs is then given by [18]: logical- ndSubscriptiSuperscriptup erCup erB aseline qualstimesInStarFactionup erPrleft-parenthesi cSubscriptiBaselinetimesequals1timesvertical-barStarSetnormalup erLamdaSubscriptuBaselinetimesEndSet1timesles -than-orequal-toutimesup erKcom aStarSetnormalup erLamdaSubscriptuBaselineEndSet1timesles -than-orequal-toutimesup erKright-parenthesi Overup erPrleft-parenthesi cSubscriptiBaselinetimesequals0timesvertical-barStarSetnormalup erLamdaSubscriptuBaselinetimesEndSet1timesles -than-orequal-toutimesup erKcom aStarSetnormalup erLamdaSubscriptuBaselineEndSet1timesles -than-orequal-toutimesup erKright-parenthesi EndFraction

equalstimesInStarStarFactionsigma-sum ationUdersciptciequals1timescom acSubscriptBaselin SubscriptuBaselin equalsdeltaSubscriptuBaselin Endscriptsexptimeslft-parenthesi gma-sum ationUdersciptuequals1OversciptuperKEndscriptsleft-parenthesi 2deltaSubscriptuBaselin minus1right-parenthesi tmesStarFaction ormaluperLamdaSubscriptuBaselin Over2EndFraction mesplustimes igma-sum ationUdersciptuequals1OversciptuperKEndscriptsleft-parenthesi 2timescirled-plusUndersciptvnot-equalsuEndscriptsdeltaSubscriptvBaselin minus1right-parenthesi tmesStarFaction ormaluperLamdanot-equalsuOver2EndFractionright-parenthesi OverOversigma-sum ationUdersciptciequals0timescom acSubscriptBaselin SubscriptuBaselin equalsdeltaSubscriptuBaselin Endscriptsexptimeslft-parenthesi gma-sum ationUdersciptuequals1OversciptuperKEndscriptsleft-parenthesi 2deltaSubscriptuBaselin minus1right-parenthesi tmesStarFaction ormaluperLamdaSubscriptuBaselin Over2EndFraction mesplustimes igma-sum ationUdersciptuequals1OversciptuperKEndscriptsleft-parenthesi 2timescirled-plusUndersciptvnot-equalsuEndscriptsdeltaSubscriptvBaselin minus1right-parenthesi tmesStarFaction ormaluperLamdanot-equalsuOver2EndFractionright-parenthesi End FractionequalsnormaluperLamdaSubscript Baselin plusnormaluperLamdaSubscript Supersciptext

After combination, the new LLR is the sum of the original LLR plus an extrinsic information independent from the original information. Note that the same

Figure 2. Receiver scheme with STECC detection

Figure 3. Receiver scheme with iterative decoding

calculation can be done to obtain an updated LLR for each bit of the combined FEC codewords. The bottleneck of this receive structure lies in the detection part whose complexity becomes rapidly prohibitive when the modulation order and/or the parameter K increase.

2.3. The turbo equalisation principle To reduce the complexity without degrading performance, we apply the turbo equalisation principle [ 17] to the STECC decoding. This principle is based on the cooperation of an equaliser stage and a decoder stage exchanging extrinsic information in an iterative way in order to compute more reliable outputs. We use the classical structure based on a minimum mean square error interference cancellation linear equaliser (MMSE-IC-LE) and add combiner stages (CB1 and CB2) to exploit the STECC structure after the equaliser and the decoder as shown in Figure 3.

We present the computation results of the three important stages (MMSE-ICLE, SBC and BSC) with perfect CSI knowledge at the receiver. More details on the calculations can be found in [18]. 2.3.1. MMSE-IC-LE stage At one iteration, the MMSE-IC-LE uses the receive signal r and the soft symbols m coming from the previous iteration to compute a new estimation of the symbols: m

The nt × nr matrix W equalises the channel H, while the nt × nt matrix Q deals with the interference coming from the symbols m when the symbol sk is estimated (1 ≤ k, i ≤ nt). One constraint over Q is that its diagonal coefficients are zeros. Both W and Q are computed using the MMSE criterion between each sent symbol sk and its estimate m: timesStarLyoutEnlargedlft-brace1stRow Subscriptlef-parenthsi kcom aperiod ght-parenthsi equals igmaSub scriptsSub perscipt2Subscript mesuperHSub scriptlef-parenthsi perodtimescom akright-parenthsi Sub persciptu erHSubscriptnormaluperASub scriptkSub persciptnegative1SubscriptBaselin 2dRownrmaluperASubscriptkBaselin tmes qualstimeslft-parenthsi gmaSubscriptSuersciptBaselin SubscriptsSuperscipt2Baselin m us igmaSubscriptSuersciptBaselin SubscriptsoverbaSuperscipt2Baselin rght-parenthsi tmesnormaluperHSupersciptnormaluperHBaselin ormaluperHtimesplu times igmaSubscriptSuersciptBaselin SubscriptsoverbaSuperscipt2Baselin tmesnormaluperHSubscriptlef-parenthsi perodtimescom akright-parenthsi Baselin tmesnormaluperHSubscriptlef-parenthsi perodtimescom akright-parenthsi SupersciptnormaluperHBaselin tmesplu times igmasqurednormaluperISubscriptnSub script SubscriptBaselin EdLayoutSarLyoutEnlargedlft-brace1stRowqSubscriptk Baselin qualstimes02ndRowSubscriptqSub scriptk Sub SubscriptSub scriptSubscript mes qualstimesnormaluperWSub scriptlef-parenthsi ktmescom aperiodSubscriptSub script gh-parenthsi tmesSubscriptnormaluperHSub script eriodtmescom aiSubscriptSuersciptEndLayout

A(k,.), A(.,k) and AH denotes the kth row, the kth column and the transpose conjugate of a matrix A respectively, In is n n identity matrix and At the first iteration, as no information about the interfering modulation symbols is available, the vector m is filled with zeros and the equaliser stage is equivalent to an usual MMSE filter. In the case of perfect knowledge of m , we talk about the genie-equaliser which represents the optimal performance of the turbo equaliser. where

×

m

2.3.2. Symbol to bit converter stage For 1 ≤ k ≤ nt, the kth estimated symbol at the output of the MMSE-IC-LE is given by: ModifyingAbovesWithcaretSubscriptkBaselinetimesequalswSubscriptleft-parenthesi ktimescom aperiodright-parenthesi Baselinetimesup erHSubscriptleft-parenthesi periodtimescom akright-parenthesi BaselinesSubscriptkBaselinetimesplusnormalup erSigmaUnderscriptiequals1timescom ainot-equalskOverscriptnSubscript BaselineEndscriptstimeswSubscriptleft-parenthesi kcom aperiodright-parenthesi Baselineup erHSubscriptleft-parenthesi periodcom airght-parenthesi Baselineleft-parenthesi sSubscriptiBaselinetimesminus overbarSubscriptiBaselineright-parenthesi timespluswSubscriptleft-parenthesi periodktimescom aperiodright-parenthesi BaselinetimesntimesequalsgSubscriptkBaselinesSubscriptkBaselinetimesplusetaSubscriptkBaseline

where gk is real and represents the MMSE-IC-LE gain whereas ηk is assumed to be a complex AWGN containing the usual complex AWGN n and the interference from the other symbols (i ≠ k). As we have independent estimation of the nt modulation symbols, the symbol to bit converter (SBC) can compute LLRs for each bit associated to one modulation symbol using in addition the a priori information coming from the previous iteration (extrinsic output of the second combiner stage). normalup erLamdaSubscript Supersciptu perSup erBup erCBaselin timesSubscriptSupersciptBaselin equalstimeslntimesStarFactionsigma-sum ationU dersciptel ment-ofup erS ubscriptu perMBaselin timescom acSubscript Baselin equals1Endscripts left-parenthesi ModifyngAbovesWithcaretSubscriptkBaselin vertical-b rs ight-parenthesi tmesnormalup erPtimesnormalrtimesl ft-parenthesi vertical-b rnormalup erLamdaSupersciptu perCup erB2timescom aextBaselin right-parenthesi Oversigma-sum ationU dersciptel ment-ofup erS ubscriptu perMBaselin timescom acSubscript Baselin equals0Endscripts left-parenthesi ModifyngAbovesWithcaretSubscriptkBaselin vertical-b rs ight-parenthesi tmesnormalup erPtimesnormalrtimesl ft-parenthesi vertical-b rnormalup erLamdaSupersciptu perCup erB2timescom aextBaselin right-parenthesi EndFraction

where: pleft-parenthesi ModifyngAbovesWithcaretSubscriptkBaselinevertical-barsright-parenthesi timesequalstimesexptimesleft-parenthesi minusStartFractionStartAbsoluteValueModifyngAbovesWithcaretSubscriptkBaselinehyphengSubscriptkBaselinesEndAbsoluteValuesquaredOversigmaSubscriptetatimeskSuperscript2BaselineEndFractionright-parenthesi timesequalstimesexptimesleft-parenthesi minusStartFractionStartAbsoluteValueModifyngAbovesWithcaretSubscriptkBaselineminusgSubscriptkBaselinesEndAbsoluteValuesquaredOversigmaSubscriptsSuperscript2BaselinetimesSubscriptSuperscriptBaselinegSubscriptkBaselinel ft-parenthesi 1minusgSubscriptkBaselineright-parenthesi EndFractionright-parenthesi

normalup erPnormalrtimesleft-parenthesi svertical-barnormalup erLamdaSupersciptup erCup erB2timescom aextBaselineright-parenthesi tmes qualstimesnormalup erPiUndersciptjequals1OversciptmSubscriptbBaselineEndscripts imesnormalup erPnormalrtimesleft-parenthesi btimes qualstimesbSubscriptjSupersciptsBaselinetimestimesvertical-barnormalup erLamdaSupersciptup erCup erB2timescom aextBaselineright-parenthesi tmes qualsnormalup erPiUndersciptjequals1OversciptmSubscriptbBaselineEndscripts imestimesStarFactioneSupersciptleft-parenthesi 2timesbSuperSubscriptjSuperSupersciptsSupersciptminus1right-parenthesi tmesnormalup erLamdaSuperSubscriptjSuperSupersciptup erCup erB2timescom aext imesSupersciptSuperSupersciptSupersciptsla h2BaselineOverSubscripteBaselinenormalup erLamdaBaselineSubscriptjSupersciptup erCup erB2timescom aext imesBaselineSupersciptBaselinesla h2timesplustimesSubscripteBaselinenegativenormalup erLamdaBaselineSubscriptjSupersciptup erCup erB2timescom aext imesBaselineSupersciptBaselinesla h2EndFraction

with m the mb bits associated to the symbol s. Note that after this SBC the a priori information is subtracted from the previous LLRs before feeding the first combiner. 2.3.3. Bit to symbol converter stage The bit to symbol converter (BSC) stage computes the soft second combiner output ΛCB2. For 1 ≤ k ≤ nt,

symbols

m from the

soverba SubscriptkBaselinetimes qualstimesnormalup erEtimesleft-bracketsSubscriptkBaselinev rtical-barnormalup erLamdaSupersciptup erCup erB aseline2Baselineright-bracket qualstimesnormalup erSigmaUndersciptel ment-ofup erS ubscriptup erMBaselineUnderUndersciptEndscripts imes timesnormalup erPnormalrtimesleft-parenthesi vertical-barnormalup erLamdaSupersciptup erCup erB aseline2Baselineright-parenthesi tmes qualsnormalup erSigmaUndersciptel ment-ofup erS ubscriptup erMBaselineUnderUndersciptEndscripts imesup erStimesStarFactioneSupersciptleft-parenthesi 2timesbSuperSubscriptjSuperSupersciptsSupersciptminus1right-parenthesi tmesnormalup erLamdaSuperSubscriptjSuperSupersciptup erCup erB aseline2SupersciptSuperSupersciptSupersciptsla h2BaselineOver Supersciptnormalup erLamdaSuperSubscriptjSuperSupersciptup erCup erB aseline2SupersciptSuperSupersciptSupersciptsla h2Baselinetimesplustimes Supersciptminusnormalup erLamdaSuperSubscriptjSuperSupersciptup erCup erB aseline2SupersciptSuperSupersciptSupersciptsla h2BaselineEndFraction

3. Simulated results We consider

a QPSK MIMO transmission over a Rayleigh block flat fading channel, 2 modulation symbols and with nr = 2 receive antennas. time invariant over τ We use the STECC with K = 3 and the FEC CC(13,15), which is an 8-state halfrate convolutional code whose octal polynomial generators are 13 and 15 [12]. Each FEC codeword is 512 bit long and pseudo-randomly interleaved. The FEC decoding algorithm is the siso BCJR algorithm [19]. Receivers with STECC detection and MMSE-IC-LE iterative decoding are used. To perform fair comparison, we consider two MIMO coding schemes with the same spectral efficiency: the Alamouti [2] encoding associated with the FEC CC(13,15) and an ST-BICM [10] using the 8-state convolutional code CC(11,13,15,17) of coding rate 0.25. The same MMSE-IC-LE turbo equaliser presented for the STECC is used to decode the ST-BICM (without the combiner stages). It needs only 3 iterations to converge. The results in terms of bit error rate (BER) versus Eb/N0 for the different MIMO coding schemes are given Figure 4. =

4. Discussion 4.1. STECC performance comparison At a BER of 10−5 the STECC C3CC(13,15) with STECC detection outperforms both reference schemes. The gain is almost equal to 1.1 dB and 0.5 dB in comparison with the Alamouti scheme and the ST-BICM scheme respectively. Moreover, the STECC curve presents a better slope and thus, a better asymptotical performance, making it a really promising MIMO coding scheme. However, its complexity is M3, while the Alamouti scheme and ST-BICM with turbo equalisation have a complexity linear with M. This drawback can be overcome with the use of the iterative receiver.

Figure 4. Performance comparison STECC vs Alamouti+FEC vs ST-BICM

4.2. Iterative decoding At a BER of 10−3, we notice a gap of 0.15 dB between the iterative and noniterative curves with a slight advantage for the first one. Looking at both curves, we can conclude that the iterative receiver offers equivalent performance as the noniterative one for a simpler detection complexity. Turbo equalisation is a promising technique for future communication systems and it adapts very well to the STECC architecture. Note that the iterative receiver only needs 3 iterations to converge. Even after convergence, we do not achieve the genie-equaliser curve (dashed curve). At a BER of 10−4, the iterative curve is at 0.4 dB from the genie-equaliser curve. This is probably due to the lack of diversity in the simulated case (a flat fading channel in a 2 × 2 configuration).

5. Conclusion In this paper we have introduced a new family of space-time codes for two transmit antennas: the STECCs. They combine in an easy way K codewords from a linear FEC. The deep space-time correlation created between the 2K associated modulation symbol vectors and the FEC properties are exploited at the receiver side to improve the transmission quality.

In the example we used for two receive antennas, the STECC outperforms traditional scheme using the Alamouti encoding and the same FEC or a STBICM structure with the same spectral efficiency. Even with sub-optimal techniques to reduce the detection complexity, the STECC still presents better asymptotical performance and thus a better space-time diversity exploitation. The structure with optimal STECC detection has a complexity which grows exponentially with K and is thus difficult to use in a practical case. However, we a

have shown that the use of a turbo equalisation principle significantly reduces the detection complexity, which becomes linear with the number of modulation symbols to recover. Moreover, this iterative structure based on the MMSE criterion achieves slightly better performance than the receiver with the STECC detection.

Acknowledgments The authors would like to thank the

Brittany regional council for funding this study.

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Performance Evaluation of MIMO Multiuser Opportunistic Schemes under QoS Requirements Nizar Zorbaa,1 and Ana I. Pérez-Neirab a Centre Tecnologic de Telecomunicacions de Catalunya (CTTC), Barcelona, Spain. b Universitat Politecnica de Catalunya (UPC), Barcelona, Spain. Spatial scheduling in a multiantenna scenario is carried out through a multibeam opportunistic beamforming technique. Within a more practical perspective, this chapter presents a transmission strategy where a minimum rate per user is required, within a given time interval to satisfy maximum delay restrictions. Both demands stand as the Quality of Service (QoS) indicators for the system behaviour, and they are both presented in closed form expressions. But to simultaneously fulfil these requirements, a trade-off on the number of available users is obtained. A Cross-Layer Call Admission Control (CAC) is then proposed to regulate the number of users, where the CAC objective is to keep the Multiuser gain of the opportunistic system, while satisfying the users' QoS requirements in terms of minimum rate and maximum scheduling delay.

Abstract.

Keywords: Wireless Telecommunications, MIMO, Opportunistic Scheduler, QoS requirements, CAC.

1. Introduction In an effort to benefit from both the opportunistic scheduling gain and the Multiple Input Multiple Output (MIMO) technology in multiuser scenarios, the Multibeam Opportunistic Beamforming (MOB) strategy has been suggested [1] to boost the wireless link capabilities, showing a high rate performance, and at the same time low complexity design. Once the rate benefits of the MOB scheme have been stated in several works in the literature [1], it turns to be the time to analyze its QoS performance and suitability for implementation in realistic commercial systems, where the costumers demand some QoS requirements for their correct operation. A practical measure of the system QoS is through the minimum rate per user 2 so [ ], that each served user is guaranteed a minimum Signal-to-Noise-InterferenceRatio (SNIR), which ensures a predefined Packet Success Rate (PSR) in the data decoding process. Concerned with the minimum QoS requirement per user, previous studies [3 ] have shown that the user satisfaction is insignificantly increased by a performance higher than its demands, while on the other hand, if the provided resources fail to guarantee its requirements, the satisfaction drastically decreases. Thus, a good scheduling scheme consists in providing service to the highest possible number of users, as long as their QoS minimum requirements are satisfied [4 ]. 1 Corresponding Author: Contact by email [email protected]

DOI: 10.1201/9781003336853-26

Performance Evaluation of MIMO Multiuser Opportunistic Schemes

Moreover, the wireless operators realize that some users cannot provide good channel conditions for communication, and delivering service to such users can be very expensive in terms of system resources; so that if these users are dropped, the operator can offer better service to all the remaining users in the system. Based on this practical point of view, operators fix some probability of failure in the QoS satisfaction, known as probability of outage [5], making all the commercial systems to have a degree of freedom that the system exploits in the satisfaction of the users’ QoS requirements. Providing QoS in the wireless environment is a difficult aspect due to the dynamic (and random) nature of the wireless channel. This task is even harder in opportunistic systems, as the users’ access to the service is not guaranteed. Previous studies [6] considered the QoS in multiuser systems through a frame division into two sections, one for the QoS satisfaction operated by round robin policy, while the other section applies opportunistic scheduling. This comes at expenses of the opportunistic multiuser gain, as the round robin strategy does not benefit from the multiuser availability. Another proposal for QoS in opportunistic systems suggests the use of weighted scheduling [7], to supply service to all the users in the system, but this approach also decreases the system multiuser gain. Therefore, a scheme that can profit from the opportunistic multiuser gain, while providing QoS, is an attractive and challenging task. This challenge is even larger in the MOB scheme, as this technique exploits the multiuser gain while it looks to benefit from its spatial multiplexing mechanism, to provide service to several users at the same time, where the users interfere among themselves. The increase in the number of available users in the system enables a proper search over the set of least interfering users, thus decreasing the interference and achieving high system data rate. However, from a practical point of view, having a large number of users in the system can be damaging for the system performance when QoS delay concerns are considered. As more users in the system, then each user has to wait for a higher time until it is provided service, making the access delay to increase beyond practical bounds. Notice the existence of a trade-off on the number of users, as increasing the number of users in the system is beneficial in terms of the system rate, but at the same time larger QoS scheduling delay is obtained. Thus, the control of the number of users is a challenging aspect, but definitely required for these schemes. The task of controlling the number of users in the system is usually developed by the Call Admission Control (CAC) unit [8 ] in the high layers of the communication process, but the application of CAC to the MOB technology needs an alternative policy, as MOB is a physical layer policy that benefits from the instantaneous channel conditions. Therefore a Cross-Layer admission process is required for the MOB technology, to accept the number of users which the system can guarantee their QoS requirements, taking into consideration the physical layer instantaneous characteristics. Whilst there exist huge contributions on CAC in the literature, very few of them deal with the opportunistic systems [9 ], and no one has presented CAC proposals for the MOB scheme. Almost all previous studies provide results on average delay and expected rate, but the maximum acceptable delay and minimum guaranteed

3. Multibeam Opportunistic Beamforming (MOB)

rate are compulsory for practical system QoS implementation, therefore, they are both derived and considered in the CAC design.

2. System Model We focus

the single cell Downlink channel where N receivers, each one of them with a single receiving antenna, are being served by a transmitter at the equipped Base Station (BS) provided with nt transmitting antennas, and supposing that N is greater than nt. A wireless multiantenna channel h[1x nt] is considered between each of the

on

and the BS, where a quasi-static block fading model is assumed, which keeps through the coherence time, and independently changes between consecutive time intervals with independent and identically distributed (i.i.d.) complex Gaussian entries ~CN(0, 1). Therefore this model captures the instantaneous channel fluctuations over each coherence time, where all users are assumed to keep fixed during each fading block, and allowed to move from block to block. Let x(t) users

constant

be the

nt x

1 transmitted vector, while denote yi(t)

as

the ith

user

received

signal

given by +Z=hyi(t)X()t (1)

where zi(t) is an additive Gaussian complex noise component with zero mean and E{|zi|2}= σ2. The transmitted signal x(t) encloses the independent data symbols si(t) to all the selected users with E{|si|2}= 1. A total transmitted power constraint Pt is considered, and for ease of notation, time index is dropped whenever possible.

3. Multibeam Opportunistic Beamforming (MOB) A practical transmission technique in multiuser MIMO scenarios is the MOB technique [ 1 ], where the BS generates nt random beams to simultaneously serve more than one user. The beam generation follows an orthogonal manner to decrease the interference among the served users. Within the acquisition step, each one of the beams is sequentially transmitted, which allows the users to calculate the SNIR related to each beam. Every user feeds back only the best SNIR to the BS together with an integer indicating the index of the selected beam. To extract the multiuser gain from the scenario, the BS scheduler chooses the user with the largest SNIR value for each one of the beams. After that, the BS enters the transmission stage and simultaneously forwards every one of the nt selected users with its intended data, where no user can obtain more than one beam at a time. Through this low-complexity transmitter processing and at the same time, an opportunistic user selection based on the instantaneous SNIR values, the MOB strategy achieves high system sum rate by spatially multiplexing several users at the same time, making the transmitted signal to be as normal x times equals times StartRo t StartFraction 1 Over n t EndFraction EndRo t imes normal up er Sigma Underscript m times equals 1 Overscript n t Endscripts times normal b Subscript m Baseline s Subscript m Baseline

(2)

with bm asthe unit-power beam assigned to the mth user, where the square root term is due to a total power constraint of Pt 1. Even MOB is shown to be non-optimal, but its low complexity and high performance make it very attractive for commercial implementation, where its single beam version is currently commercialized in UMTS-EISDPA and Qualcomm's HDR systems. —

The simultaneous transmission generates interference among the serviced users, so that this scheme is characterized by its SNIR term. Even though the beams are orthogonally generated, some of this orthogonality is lost in the propagation channel [1], making the SNIR formulation for the ith user through the mth beam to state as up erSup erNup erIup erRSubscripti mescom amBaselinetimesequalstimesStarStarFactionStarFaction1OverntEndFractionStarAbsoluteValuenormalhSubscriptBaselineSubscripti mesBaselinetimesnormalbSubscriptmBaselineEndAbsoluteValuesquaredOverOversigmasquaredplus igma-sum ationUnderscriptunot-equalsmOverscriptntEndscriptsStarFaction1OverntEndFractionStarAbsoluteValuenormalhSubscriptiBaselineSubscriptBaselinenormalbSubscriptuBaselineEndAbsoluteValuesquaredEndEndFraction

(3)

where a uniform power allocation among all the users is considered, as the small amount of feedback does not allow for power allocation over the transmitting beams. Along this work, all the users are assumed to have the same average channel characteristics, and showing the same distribution for the maximum SNIR value, so that each user has the same probability to be selected. If this is not the case (e.g. heterogeneous users’ distribution in the cell, with some users far from the BS), then a channel normalization (e.g. division by the path loss) can be accomplished for such a scenario. Notice that the users’ selection process is defined by a search over the instantaneous SNIR values to select the best user for each generated beam. As more users are available, the system multiuser gain is larger so that higher rate performance is expected, to the extent that when the number of users gets close to infinity, the MOB technique becomes capacity optimal [1]. However, as previously commented for practical applications, the number of available users has to be restricted for delay considerations. This generates a trade-off on the number of users, as later shown.

4. System QoS Performance As the MOB scheme is shown to be beneficial for the system sum rate, it turns to be the time to analyze its QoS performance. Based on the design objectives and restrictions, several metrics or indicators can characterized the QoS behaviour, so that QoS can be in terms of rate, reflecting the minimum required rate per user; or QoS in terms of delay, showing the maximum scheduling delay that a user can tolerate. Both concepts of QoS are considered in this chapter, where the MOB scheme guarantees a minimum rate per user, which is presented by minimum SNIR restriction (snirth) per each user in the system, and delivered to it within a maximum time delay. As already commented, the objective in this work is to extract all the opportunistic multiuser gain, while the QoS requirements are obtained in terms of minimum rate and maximum scheduling delay. For the implementation of the MOB scheme in commercial systems, a practical service policy is adapted, where a predefined probability of outage ξoutin the service

is tolerated [ 5], as done in cellular GSM and UMTS systems, and expected in broadband networking standards (IEEE 802.11 n, IEEE 802.16e, 4G, ...) when running delay-constrained applications. This chapter defines two concepts for outage. The first one is related to the opportunistic access policy and the time instant when the ith user is provided service. The user opportunistic access is characterized in Section (4.1), where it is obtained the expression for its access delay probability. The second outage concept accounts for the received data rate once the ith user is selected for transmission, and whether its rate requirement is satisfied or not. Section (4.2) derives the service SNIR distribution for the selected user, which enables to present the minimum guaranteed rate under an outage ξrate.

4.1. Access Delay Outage This section identifies the maximum access delay (in time slots) until the user is served through any of the nt generated beams at the BS. Therefore, if an active user is in the system, but it does not access the channel within its maximum allowed delay, this chapter declares it as being in access delay, with an outage probability ξaccess given by =

ξaccess

1

-

V(K) (4)

with V(K) as the probability that a maximum of K time slots are required to select a user i from a group of N i.i.d. users, where this probability follows a Geometric Distribution [10] as (5) upper V left-parenthesis upper K right-parenthesis times equals times 1 minus left-parenthesis 1 minus upper P overbar Subscript a c c e s s Baseline right-parenthesis Superscript upper K

In the MOB

scheme, each one of the N independent users tries to access the beams with Paccess nt/N, therefore from previous equation, the maximum number of time slots K until the ith user is selected for transmission, with a probability of delay outage ξaccess, is given by nt

generated

=

up er K times equals StartFraction log times left-parenthesi 1 hyphen up er V right-parenthesi Over log times left-parenthesi 1 minus up er P overbar Subscript a c e s Baseline right-parenthesi EndFraction times equals times StartStartFraction log left-parenthesi xi Subscript a c e s Baseline right-parenthesi OverOver log times left-parenthesi 1 minus StartFraction t Over up er N EndFraction right-parenthesi EndEndFraction

(6) where the effects of the number of active users N and the number of serving beams nt, are shown. 4.2. Minimum Rate Outage Even a user is selected for transmission, but its received rate may be below its requirement, therefore generating a rate failure with the consequent rate outage to that user. This work calculates the distribution of the serving SNIR, to characterize the rate outage ξrate. As the MOB philosophy provides service to the users with the best channel conditions, thus the serving SNIR value is the maximum SNIR over the active users in the system corresponding to each generated beam. From the SNIR equation in (3) with nt transmitted beams, its numerator follows a Chi-square χ2(2) distribution while the interference terms in the denominator are modelled as χ2 (2{nt 1)). Using —

these distributions, the SNIR cumulative distribution function (cdf) is obtained as [1][2] up er F left-parenthesi x right-parenthesi times equals times 1 minus StartFraction e Superscript minus left-parenthesi x times period times igma squared n t right-parenthesi Baseline Over left-parenthesi 1 times plus times x right-parenthesi Superscript n t minus 1 Baseline EndFraction

(7) and since the serving SNIR is the maximum over all the users’ SNIR values, then the serving SNIR cdf is stated as up er F up er F left-parenthesi x right-parenthesi times equals times left-parenthesi up er F left-parenthesi x right-parenthesi right-parenthesi Superscript up er N Baseline times equals times left-parenthesi 1 minus StartFraction e Superscript minus left-parenthesi x times period sigma squared n t right-parenthesi Baseline Over left-parenthesi 1 times plus times x right-parenthesi Superscript n t minus 1 Baseline EndFraction right-parenthesi Superscript up er N

(8) Therefore, achieving the minimum required SNIR snirth for each serviced user with a predefined rate outage ξrate as xi Subscript r a t e Baseline times equals times left-parenthesi 1 minus StartFraction e Superscript minus left-parenthesi times n i r Super Subscript h Superscript imes period sigma squared n t right-parenthesi Baseline Over left-parenthesi 1 times plus times n i r Subscript h Baseline right-parenthesi Superscript n t minus 1 Baseline EndFraction right-parenthesi Superscript up er N

(9) and by fixing the number of users N, the values of snirth and ξrate can be computed on the basis of any system objectives. With further manipulations, the expression (9) can be re-formulated as up er R times equals times log times left-parenthesis 1 times plus times s n i r Subscript h Baseline right-parenthesis times equals times StartStartFraction log times left-parenthesis StartFraction 1 Over 1 minus RootIndex up er N StartRo t xi Subscript r a t e Baseline Subscript Baseline EndRo t EndFraction right-parenthesis times hyphen s n i r Subscript h Baseline times period times sigma squared n t OverOver n t hyphen 1 EndEndFraction

(10) obtaining the minimum guaranteed-rate. It shows the rate limits of the system, indicating that high outage ξrate. in equation (10) is obtained when large snirth, values are demanded, otherwise the right hand term becomes negative, thus indicating the requirements unfeasibility. Notice that the minimum SNIR ensures the user’s decoding process to be successful, where a unit step function is used for the detection procedure, making the PSR to relate to snirth as up er P up er S up er R times equals times left-brace StartLayout 1st Row 1 times i f times s e r v i n g times up er S up er N up er I up er R times greater-than-or-equal-to s n i r Subscript h Baseline 2nd Row 0 times i f times s e r v i n g times up er S up er N up er I up er R times greater-than-or-equal-to s n i r Subscript h Baseline EndLayout imes

(11) and a direct relation to ξrate is obtained from equation (9). This PSR approximation is very practical, as the signal coding and decoding procedures are incorporated in this formulation. Even more developed PSR expressions are available in literature, accounting for further steps in the communication process, but for the purposes of current chapter, this approximation is valid. 4.3. System Outage As previously explained, two different outage measures control the MOB scheme, but a single parameter is desired to define the total system performance. Notice that the two discussed kinds of outage are totally independent, as the user does have

access to the channel when its SNIR is the maximum with respect to a given beam and over all the other users, but being the user with largest SNIR does not provide any guarantee that this SNIR is larger than a given threshold snirth. Therefore, the total outage ξout is defined as ξout

=

1 -(1

-ξaccess) (1 .

-ξrate)(12)

standing as the global measure of system outage. 4.4. Maximum Scheduling Delay The maximum scheduling delay can now be obtained, as the scenario outage has been defined. Having a packet of length W bits waiting for transmission at the BS scheduler and corresponding to the ith user, this chapter defines the maximum scheduling delay as the maximum required time to make the packet to be correctly received at its destination. The smallest transmission unit is a packet, so that the whole packet is transmitted or it remains at the BS buffer. In opportunistic systems, the scheduling (service) delay is more important than the queue delay consideration because in opportunistic systems, the user does not have any guarantee for access, as done in TDMA or in single user scenarios. Furthermore, in multiuser scenarios, a user requests service when it has enough packets for transmission/reception, so that all potential users have the minimum number of packets in their queues. Thus, the chapter focuses on the scheduling delay, and both the buffer management and source statistics for arriving packets are not addressed [11]. This makes the scheduling delay study to be only related to the first packet in each user’s queue, which is actually the packet suffering the maximum scheduling delay. Therefore, the queues stability target [12] is not considered. Notice that the delay resulting from the access process (i.e. the opportunistic selection) together with the delay caused by the channel instantaneous condition (i.e. when the serving SNIR is below the minimum required threshold) are both enclosed in the scheduling delay definition, therefore providing a general expression for scheduling delay in the MOB scheme. In the previous section, it is obtained that the maximum number of time slots to select a user is equal to K, and under a predefined access delay outage, where this access actually provides a minimum rate R under a known rate outage. Therefore, with a global outage ξout, the maximum scheduling delay is equal to the K access slots formulation in (6) as maximum scheduling delay equals times StartFraction log times left-parenthesis xi Subscript a c c e s s Baseline right-parenthesis Over log times left-parenthesis 1 hyphen n t slash normal upper N right-parenthesis EndFraction

(13) showing the effect of the optimization variables. To avoid misleading conclusions for the reader, it is convenient to present a numerical example, so that in a scenario with 30 total users, nt 1 M Hz, K 25 required N 3, a system bandwidth of Bw 1 and R maximum delay, σ2 580Kbps minimum demanded rate for each user, it results that ξaccess 7.1% and ξrate 4.3% are obtained. Therefore, a wireless =

=

—

=

=

=

=

=

operator can guarantee to each user, the correct reception of its packet within a maximum scheduling delay of 25 slots and with a total outage of ξout = 11.0%. 4.5. User Guaranteed Throughput Notice that increasing the number of users N makes the minimum rate R to grow. But at the same time, a larger N induces higher scheduling delay. This shows a trade-off on the number of available users in the scenario, as a high number of users is not always beneficial to the system, when asking for QoS demands. A common measure to evaluate the QoS performance is desired, where the per-user guaranteed throughput stands as the most appropriate metric. But the throughput concept in multiuser opportunistic systems has a different flavour from the corresponding to the single user case. When a single user scenario is considered, then all the resources are targeted to the same user, and over all the time. Therefore, the notion of throughput is related to the total amount of packets that the system can correctly transmit per second [13]. On the other hand, in opportunistic scenarios the throughput shows a different concept. As the user is not always served, then that user receives a zero throughput over several time slots until it is serviced. Therefore, a normalized throughput over the time is required. Notice that this definition of throughput accounts for the waiting time and hence, for the corresponding scheduling delay expression. Obtaining the user throughput formulation is difficult as several processes are included in the communication procedure. The receiver decoding through the unit step function in equation (11) simplifies the throughput formulation, as the effects of several steps in the communication process (e.g. coding) are avoided. Hence, with a system bandwidth Bw and ts as the slot service time (assumed to match the channel coherence time), the minimum guaranteed-throughput for each user in the system, defined in bits/slot, states

as

up erTtimesequalstimesup erBSubscriptwBaselinetimestSubscriptBaselineSubscriptsBaselinetimesStartFractionup erROverup erKEndFractiontimesequalstimesStartSartFractionup erBSubscriptwBaselinetSubscriptBaselineSubscriptsBaselinetimeslogtimesleft-parenthesi 1minusStartFraction tOverup erNEndFractionright-parenthesi timeslogtimesleft-parenthesi StartFraction1Over1minusRo tIndexup erNStartRo txiSubscriptrateBaselineEndRo tEndFractionright-parenthesi minus nirSubscript hBaselinetimesperiodtimes igmasquaredntOverOverleft-parenthesi ntminus1right-parenthesi timeslogleft-parenthesi xiSubscriptac es Baselineright-parenthesi EndEndFraction

(14) providing a closed form solution for the throughput, with all the operating variables.

5. Cross-Layer CAC Due to the users’ perception towards network reliability [ 14], blocking a new user is much better than admitting it and make it susceptible to deficient QoS guarantees, which can cause a connection drop [ 8], Therefore, to guarantee the QoS requirements for the accepted users in the system, the CAC operation is required to achieve the system efficiency by exploiting the available network resources.

As the MOB scheme shows a high dependence on the number of available users in the system, then the CAC role is further stressed to position the system in the best operating point of the trade-off on the number of users. But as MOB

considers the users’ SNIR for its operation, then the CAC has to further account for the instantaneous SNIR channel indicator through a Cross-Layering CAC policy. Notice that within the number of users trade-off, not all requirements are feasible, as a very low delay demand together with a very high required rate are impossible to achieve at the same time, thus defining a feasibility region for the CAC operation, as later shown in the simulations section.

This section presents a Cross-Layer CAC strategy for the MOB scheme, where the CAC goal is to increase the system multiuser gain, through accepting the maximum number of available users, but restricted to guarantee their QoS, obviously under a certain outage, as

(15)

where Dmax denotes the maximum allowed scheduling delay, while Tmin reflects the minimum throughput demanded by every user. Notice that each one of the restrictions is expressed in a closed form formulation, thanks to the previously obtained equations. This CAC policy for the MOB scheme keeps the opportunistic multiuser gain through the best SNIR selection over all the beams, while the users QoS requirements are satisfied. And to achieve both targets, the number of users is optimized as shown in expression (15), where the reader can realize the effect that all the previous exposed variables have on this Cross-Layer CAC performance. This optimization provides a method to prevent system congestion by controlling the maximum number of users that the network can support, where congestion degrades the system performance as it induces QoS failure and network collapse. From another point-of-view, it provides a tool for network dimensioning engineers, as the system designer can calculate the required number of cells to cover a certain population area. Several applications can coexist in the system, with different QoS requirements for each application. A pre-optimization process can be accomplished for such scenario, where a portion out of the total system resources (e.g. bandwidth) can be used to satisfy the QoS requirements of each application, and then the number of active users running each application is optimized. Even such approach is not optimal but it is very practical, as the commercial operators assign each application a percentage of the available resources, based on the revenues business-model fixed by the operator. A small comment to avoid disorientation, as the reader can wonder about the existence of two user selection processes, the one in this section and the previously commented in section (4.1). Notice that the customer that wants to set up a connection has to pass through two selection processes, in the first one it asks to access the network (task accomplished by the CAC operation). Once the user is in the network (i.e. active), a search for the user showing the best channel with respect to

Figure 1. The system scenario with a two-steps selection example

each generated beam is required, where this second selection process is performed through the MOB scheduler. A graphical explanation of this scenario is presented in Figure 1, where a two-steps selection example is shown.

6. Numerical Results The performance of the discussed scheme is presented by Monte Carlo simulations where both QoS requirements, in terms of minimum SNIR per user and within a maximum time of K slots, are guaranteed by the serving policy. We consider a Downlink single cell wireless scenario with nt = 2 transmitting antennas and a variable number of active users. The transmitter runs the MOB technique where two orthogonal beams are set up. A system bandwidth of 1 MHz with ts = 1 msec are considered. A total transmitted power Pt = 1 is used and a noise variance of σ2 = 1 is also assumed, where a packet length of W = 160 bytes is tackled in the simulations. Concerned with the rate outage in the MOB scheme, Figure 2 plots the ξrate parameter for different values of minimum rate. It is evident from the mathematical formulation in (10) that a higher outage ξrate is obtained when the user requirement increases, a matter that is confirmed by the simulations. The obtained results along this chapter are based on exact formulations, so that the simulated results must match the theoretical values, as seen in Figure 2. To show the effect of the multiuser gain on the outage performance, two numbers of active users are considered in the cell. Notice that a higher number of available users generates lower rate outage, as the scheduler has more freedom to choose a better set of users to meet their requirements.

Figure 2. The system performance with rate outage

Figure 3. The system maximum scheduling delay in outage scenarios

Regarding the maximum scheduling delay performance, Figure 3 shows it for different values of outage, where the maximum scheduling delay is decreased for a larger allowed outage. A variable number of active users is available in the scenario, where it is seen that the largest scheduling delay is obtained when running a large

Figure 4. The minimum guaranteed-throughput

number of users with a small outage value. Notice that for a system with two users, the scheduling delay is zero as they are serviced through the two generated beams. An appropriate system metric in the MOB scheme is the normalized throughput, where as already commented, a user is not serviced over all the time. Related to the minimum guaranteed-throughput in equation (14), Figure 4 exhibits its results for different number of active users simulated over several allowed total outage ξout. It presents a very interesting result, as it shows that there is an optimum number of users, where the guaranteed throughput has a maximum value for each considered outage. The obtained results are explained by the presented number of users tradeoff where as previously seen in Figure 2, more users decrease the rate outage, but at the same time, Figure 3 showed that each user has to wait for a longer time to have access to the network, as more users are in the network. The joint effect of the two driving forces is obtained through the formulation of the throughput, where Figure 4 reflects that for an outage ξrate = 2%, a large number of users is beneficial due to the multiuser gain, but only until a given point (15 user in the plot); and after that point, the increase in the number of users does not compensate for their disadvantage in access delay. As higher outage value is allowed, it indicates that the system has more freedom to unsatisfy the users’ QoS demands, so that the multiuser gain has a lower effect in the system. Therefore, a smaller number of users is the optimal solution for an increased outage value. Now dealing with the main motivation of this chapter, Figure 5 shows the CAC performance under different QoS requirements, where the number of users that can be accepted in the system is based on 1.-the minimum rate to the right hand side of the plot, and 2.-the maximum allowed scheduling delay to the left hand side of the plot. The results state that if a maximum scheduling delay of 28msec and a minimum rate of 700Kbps are required, then a maximum of 20 users can be accepted

Figure 5. The CAC performance

in the system. The plot is presented in terms of delay and rate regions so that, all minimum rates below 700Kbps are also possible for 20 users, and the same applies for the scheduling delay. For the considered scenario, Figure 5 provides a detailed view for the system designer to realize the system capabilities, and optimize the CAC operation based on the system maximum scheduling delay and minimum rate restrictions. The obtained results are very interesting as they also show the feasibility region of the presented CAC, where as previously commented, a very large rate together with a small delay are impossible to obtain at the same time. This provides the system trade-off between minimum rate and maximum scheduling delay, where the commercial operators can position themselves on the most convenient point, based on their requirements and restrictions.

7. Conclusions performance is evaluated in an outage scenario, where a predefined QoS failure is allowed in the users’ service. Two sources of outage are considered along this work: from the opportunistic users’ access process and due to the fading channel characteristics. The QoS requirements are defined in terms of minimum rate and maximum scheduling delay, where the designer objective is to obtain all the system The MOB

multiuser gain, while QoS guarantees are provided to the users. A trade-off over the number of available users is obtained when both requirements are desired, so that a CAC is presented to control the number of users in the system while their QoS demands are guaranteed.

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Applications Services and Business Models John Soldatosa a Athens Information Technology, Peania, Greece Abstract. This section presents applications and services that utilize technology building blocks introduced in earlier sections. To this end, it includes contributed chapters emphasizing on wireless and mobile networking applications, services and business models. The presented applications span a variety of application domains, including Localization and Tracking, Vehicular Communications and Personal Networks. Apart from manifesting the wealth of wireless networking applications, the section demonstrates that alternative wireless networking approaches and technologies can be used for the same problem in different scenarios and contexts. This is achieved through a clusterof chapter that propose alternative localization and tracking techniques based on different technologies.

Section Overview Earlier sections of this volume have emphasized on a wide range of wireless technologies including radio Resource Management, Quality of Service (QoS), Channel Modelling, MIMO and OFDM. These technologies are key building blocks for numerous mobile and wireless applications, while at the same time enabling revenue generating business models for service providers and network operators. This section of the volume presents a collection of indicative wireless networking applications, which manifests the potential of the above mentioned technologies. The presented applications fall under the following areas: Localization and Tracking, Vehicular Communications and Personal Networks. Furthermore, a QoS aware business model based on adaptive billing schemes is also discussed. Since they span different application domains, this section manifests also the wealth of wireless networking applications. Moreover, given that three chapters focus on localization and tracking, we also demonstrate that wireless technologies offer alternative approaches and disciplines to solving the same problem.

The three chapters on localization and tracking are clustered together at the beginning of this section. The first of these articles is titled “Metric Multidimensional Scaling for Localization and Tracking” and co-authored by David Macagnano, Giuseppe Destino, and Giuseppe Abreuc. The authors introduce a metric multidimensional scaling (MDS) approach towards solving the localization problem. To this end the authors introduce the core theoretical concepts of MDS, paying special attention on the Classical solution, as well as on the Least Squares approach for metric scaling. Moreover, they illustrate the tracking problem in an MDS context in a way that separates the localization and the tracking problems. Accordingly, they prove the benefits of a Classical scaling (eigenproblem) approach

DOI: 10.1201/9781003336853-27

Applications Services and Business Models for solving the tracking context (i.e., dynamic environment), as well as the benefits of a Least Squares approach (based on the optimization of a stress objective function) to solve the static localization problem.

The second chapter on localization co-authored by Yong Bai, Lan Chen is focused on a technique for obtaining node positions in ad-hoc networks, as a foundation for location based context-aware services. Specifically, the chapter is titled “Localization in Ad Hoc Networks for Mobile Ubiquitous Service Provisioning” and focused on Segmentation-aided and Density-aware Hop-count (SDH) algorithm, which improves the accuracy in estimating node locations. The chapter introduces the algorithm and applies it in the case of mobile nodes based on a relative location estimation method that requires no knowledge of the location map of the whole network. The authors present numerical analysis and simulation results, which prove the benefits of the introduced algorithm over conventional techniques. Keiji Terasaka and Akihiro Kajiwara are the authors of the third chapter on localization, which is titled “Human body detection using UWB-IR indoor channel”. This chapter emphasizes on an indoor ultra-wideband impulse-radio (UWBIR) channel based human body sensing discipline. Motivated by the fact that radio with high range resolution can penetrate into the walls and also that the reflected paths from the human should be able to be discriminated in time domain, the authors propose the use of UWB-IR for protecting a house comprising four rooms. Through experimentation the authors prove that their techniques can locate the person no matter his navigation path within the house. Following the localization and tracking chapters, the chapter “An Overview of Wireless MAC Protocols for Vehicular Communications", which is co-authored by Spyridon Vassilaras, Spyros Tsevas, and Gregory S. Yovanof, presents a collection of MAC (Medium Access Control) protocols for wireless inter-vehicular communications. The authors describe the potential impact of short to medium-range communication systems (vehicle-to-vehicle and vehicle-to-roadside) on improving vehicular safety, while also enabling a range of other applications. Accordingly they present the latest developments in wireless IVC starting with DSRC and WAVE/802.11p. Furthermore, they elaborate on MAC protocol enhancements that render 802.11 protocols suitable for high mobility applications. Special emphasis is paid in describing and resolving the limitations of the CSMA/CA medium access, which make it unsuitable for delay sensitive applications (e.g., congested scenarios comprising many mobile nodes). In overcoming the above-mentioned limitations the authors refer to a set of innovative MAC designs. Overall, the chapter has also an overview nature. Hence, readers will find pointers to a wealth of sources, which could help them to explore further the field of 4G vehicular communications. Karsten Schoo, Harald Kaaja, Janne Marin, and Juha Salokannel are the authors of the chapter “WiMedia UWB Concept, Design and Implications”, which provides an overview about WiMedia UWB and presents results pertaining to the usage in mobile devices. The chapter starts with an introduction of the MAC superframe structure, as well as of key MAC features including channel access, dynamic beacon protocol, hibernation, security modes, channel selection, ranging and rate adaptation. The authors present also a collection of results concerning both —

Section Overview the functionality and the performance in all above areas. Their analysis includes also reference to weak points that are a set-back for meeting future demands. The chapter provides also insights on future enhancements that could act as a remedy for these limitations. Another chapter of this section focuses on service discovery for Personal Networks. In particular, the chapter is titled “Signalling Model of Service Discovery in Heterogeneous Personal Networks” and co-authored by Thafer H. Sulaiman, Hikmat Aldelo and Hamed S. Al-Raweshidy. The authors underpin the importance of service discovery for network performance and usability. Accordingly they introduce a signalling model for efficient services advertisement and discovery in node,

personal cluster and global levels. Moreover, they provide a simulation model for deriving results at all these levels. Their results demonstrate that as a cluster increases in size (e.g., due to the number of nodes in the network) there is only minor effect on end-to-end delay (e.g., as the cluster size is doubled the end-to-end delay increases approx. 2.5%). However, the end-to-end delay increases significantly, in cases where a considerable increase in the services activity is observed. Note that the work presented in the chapter includes also a simulation model and flowchart algorithm for node services. The last chapter of the section emphasizes on a Business Model for wireless networks. In particular, the title of the chapter is: “A Business Model for QoS Assessment in Mobile Wireless Networks” and the authors are Francesco Benedetto and Gaetano Giunta. Contrary to the earlier articles of the section that focus on specific applications and services, this chapter introduces a while business model for video call billing. The model is characterized as QoS-aware given that it is based on the end-to-end Quality of Service (QoS) derived via a tracing watermarking procedure. To this end, the authors commence the chapter with a presentation of basic frameworks of tracing watermarking for QoS assessment. Accordingly, they present the business models based on a Bayesian procedure decision making. Furthermore, they evaluate the model and present relevant numerical results for different business scenarios (i.e. mainly concerning video calling in UMTS networks). Overall the authors argue that their model can be used as a vehicle for network operators to implement adaptive billing strategies based on the quality of service observed. They also claim that such a model could generate additional profits and revenue streams.

Overall this section demonstrates the potential impact of wireless communications on a range of different applications. The latter could greatly improve our quality of life, while at the same time boosting the development of service providers and network operators. One may argue that there is a much wider range of application possibilities based on emerging wireless technologies. Nevertheless, the scope of the section is to present a sample of representative applications, rather than providing an exhaustive coverage of emerging wireless applications. We think that the readers will find the presented applications and business models interesting.

C\ Taylor & Francis ~

Taylor&FrancisGroup http://taylo ra ndfra n ci s.com

Metric Multidimensional Scaling for Localization and Tracking Davide Macagnanoa,1, Giuseppe Destinob,2 and Giuseppe Abreuc,3 Centre for Wireless Communications University of Oulu, Finland P.O.Box 4500, 90014-Finland Abstract. In this note the positioning problem is interpreted and solved through metric multidimensional scaling (MDS). It is shown how the different assumptions underling the localization and tracking problem, together with the requirement imposed by real scenario, suit the iterative optimization of a stress objective function (Least Square Scaling)inthe static context, and the solution of an eigenproblem (Classical Scaling) in the dynamic one.

1. Introduction Already in the

1930s multidimensional scaling (MDS) was introduced in psychometrika [ 1 ], [2 ] as a technique to recover the coordinates for set of points from the matrix representation of their mutual Euclidean distances. Then at the beginning of 1950s Togerson [ 3] used the aforementioned technique for Scaling, proposing what is currently known as Classical MDS. The MDS can be seen as a multivariate data analysis technique able to produce a graphical representation of a set of n objects under the condition that the set of dissimilarities (δi,j) between every two objects (i, j) is provided. More precisely,, MDS searches for a configuration of points in a given space (often Euclidean) so that the point-to-point distances match as much as possible the dissimilarities provided. Although MDS is not applicable to reconstruct maps only, in this article the usage of such a technique is investigated to solve the localization and tracking problem in a wireless network. Metric scaling, in its Classical and Least Squares solution, is shown to be an efficient and robust technique to solve the aforementioned problems. The structure of the reminder of this chapter is as follow: in section 2, the theory behind MDS is introduced, with focus on the Classical solution and the concepts behind the Least Squares approach for metric scaling, In section 3, the positioning problem in wireless network is posed into the MDS context. Due to their different requirements, the tracking/localization problems are discussed separately, showing how a Classical scaling approach can be efficiently used to solve the tracking context, while a Least Squares approach to solve the localization problem.

1 Davide Magnano, Giuseppe Destino, Giuseppe Abreu, [macagnan,destino,giuseppe]@ee.oulu.fi

DOI: 10.1201/9781003336853-28

Metric Multidimensional Scaling for Localization and Tracking

2. MDS As already introduced, MDS is a multivariate data analysis technique used to map “proximities” into a space. These “proximities”, can be distinguished between dissimilarities {δi,j} (distance-like quantities), or similarities {si,j} (inversely related to distances), and have to be chosen in relation to the problem at hand. When the dissimilarities are chosen as Euclidean distances (i.e., quantitative values), which is the case for the positioning problem, the MDS is known as Metric MDS. For a list of similarities/dissimilarities and corresponding properties, please refer to [4] and references therein. Given n points and corresponding dissimilarity {δi,j}, MDS finds a set of points in a space such that a one-to-one mapping between the original configuration and the reconstructed one exists. This is done in a way such that the inter-distances {di,j} f in the reconstructed scenario follow m with being a continuous parametric monotonic function. Depending on how much information of the original set {di,j] is available, two forms of Metric MDS can be distinguished. When all the distances are known, the original configuration is recovered by an algebraic method that performs a spectral decomposition of a double centered matrix (Classical solution), as shown [3 ]. In contrast, when only a partial subset of {di,j} is provided, then the mapping problem becomes a completion/approximation problem, that is efficiently solved by means of an optimization-based technique (Least Squares scaling).

2.1. Classical Scaling In this subsection, the discussion is focused on the algebraic solution of the metric scaling problem, refereed to as Classical Scaling. Defining with xi(i = 1 ··· n) the [1 × η] vectors containing the coordinates for the n points in a η dimensional space, and knowing that for the Classical scaling {δi,j}={di,j} holds, then the dissimilarities are expressed by ,m where the supersctipt T indicates transpose. Therefore the inner product between two objects xi, xj, belonging to the original configuration of points can be written as m . is The Classical scaling solution, once that the set of all inter-distances m provided, constructs B before, and then recovers the unknown objects coordinates as the least square solution on the inner product matrix B[ 5 ]. To overcome the indeterminacy of the solution due to translation, the centroid of the configuration is placed at the origin Now, writing and imposing the conditioned mentioned above (centroid at the origin), m m

m

it follows that .

m

into a Euclidean Distance Matrix (EDM) D[n×n], the same transformation can be expressed in matrix form through "double-centering". Indeed B X XT can be written using the objects inter-distances as m

Grouping {di,j} =

•

with D2 as the matrix of the squared distances, the “centering matrix” J defined as I J n-1 e eT, e as the |[n × 1] unitary vector, and I[n ×n] the identity matrix. In should be noticed that J defines a linear transformation and it is characterized I by the orthogonal property J JT =

—

•

•

=

3. Positioning in Wireless Networks Now, since B is

symmetric, positive semi-definite matrix of rank(B) =η, its V L VT, where V and L as the eigeneigen-decomposition, expressed by B vectors and the diagonal-eigenvalue matrix of B, allows to recover X. Indeed, due to rank(B) = rank(X• XT)= rank(X)= η, and assuming both eigenvectors and in with ordered eigenvalues descending order, B can be rewritten as B Vη Lη; m m the first η containing eigenvalues/eigenvectors. a

•

=

•

=

Therefore, it follows that is

m

,

•

•

,

which includes the recovered coordinates for the

n

(where ). Obviously corresponds objects, given by the original configuration up rigid transformations (translation, rotation and reflections) on the axes. But, if at least η + 1 reference points are known, the Procrustes m

m

m

to

transformation allows to map the solution back to the absolute reference system used. A survey on different Procrustes techniques can be found in [6 ], studies on the robustness for the Classical Scaling solutions are provided in [7 ].

2.2. Least Square Scaling In some cases only a subset of {di,j} is available, giving rise to a distance completion problem. Metric least squares scaling solves the aforementioned problem looking for a configuration of points minimizing a STRESS loss function, where possibly a continuous monotonic transformation on the dissimilarities f(δi,j) is used. An example of STRESS function, used later in this paper and corresponding to the least squares on the squared distances, is up er S up er S up er T up er R up er E up er S up er S left-parenthesi normal up er X right-parenthesi identical-to normal up er Sigma Underscript i equals 1 Overscript n Endscripts times normal up er Sigma Underscript j equals 1 Overscript n Endscripts times w Subscript i comma j times Baseline left-parenthesi delta Subscript i comma j Superscript 2 Baseline minus d Subscript i comma j Superscript 2 Baseline left-parenthesi normal up er X right-parenthesi right-parenthesi squared period times

Such a function is proven to be non-convex in the X variable; therefore, either a global optimization technique or a reliable starting point is required to avoid local minima. For other possible STRESS loss functions and techniques to solve the least square problem refer to section 3.2, [5], [8] and references therein.

3. Positioning in Wireless Networks The positioning problem, defined as the estimation of node’s locations from data sets of their inter-distance measurements, represents the natural application for the aforementioned classification technique. The association between mobile nodes in wireless network with objects, and the one between mutual Euclidean distances in the η dimensional space with the dissimilarities, allow to look at the positioning problem in a wireless network through an MDS formulation, and its solution is then, as put by Boyd et al., [9], “a matter of technology”. The main challenges to face in the positioning problem are related to the perturbation affecting the ranging (observations), the eventual incompleteness on the set of inter-distances {di,j}, and the computational complexity of the technique. As already discussed in section 2,

and how shown in the following subsection, the MDS formulation will allow to cope well with all the aforementioned problems. The general problem of mobile positioning is divided into two contexts: localization and tracking. The former denotes a scenario characterized by static or quasistatic terminals; therefore the aim is to maximize the accuracy on the location estimates. On the other hand, the latter denotes a scenario where the nodes are moving following continuous trajectories with unpredictable/variable direction and dynamic. Under these circumstances, the aim is to track the targets with enough accuracy and robustness for a large range of dynamics.

In the previous section, two metric MDS approaches are described. The Classical scaling represents an algebraic method that allows the estimation of node locations by spectral decomposition of the transformed EDM (Euclidean kernel). In [10]–[11] it is shown how, while remaining a low complex solution, the MDS-based tracking solution is a completely non-parametric approach and therefore independent from target’s dynamics. In [12], it is shown how its usage together with a prefiltering block allows that improves the performance even in harsh environments. In contrast, a least squares scaling is more suitable for a localization problem due to the presence of weights, which ensure higher robustness to imperfect and incomplete data set. 3.1. Scenarios for Localization and Tracking Localization and Tracking can be assumed to be a key application for the next generation of mobile wireless networks. It is envisioned that the 4G and beyond network technologies will integrate cellular and ad-hoc based wireless architectures. A heterogeneous ensemble of mobile terminals will be able to communicate both in a peer-to-peer and cellular based fashion, so that the network will include both meshed and star-like topologies. Therefore it can be expected that algorithms dedicated to localization and tracking will be used to exploit the resources available at their best, maybe switching from one topology to another depending on the application/requirements. Reminding that the main purpose of a localization problem is to obtain very accurate node location estimates, the most suitable scenario is a meshed network, with the nodes able to measure their mutual distances. In contrast, some of the major challenges for tracking algorithms in the wireless network contexts are stringent constraints on the power consumption of sensors activated for tracking purposes, the requirement for low-complexity algorithms, and the ability to track a potentially large number of sensors simultaneously. Thinking about the kind of application that could require a constant update on the target’s trajectories (e.g., surveillance ...), and due to the need to keep the energy consumption low, it can be preferred an anchor-to-target ranging communication, assuming therefore the existence of an infrastructure in the network including the anchor nodes. Under these assumptions a cellular based architecture (star-topology) results to be natural scenario for trackinglike applications.

3.2. Classical Scaling for Tracking discussed above, the main challenges in the tracking scenario are that targets may have different dynamics, and be in large numbers. The solution here discussed for the tracking problem is the MDS-Based algorithm originally proposed in [ 10]. Following its main features as well as its ability to cope with target’s dynamic and ranging errors will be discussed. Compared to the Classical MDS solution of Section 2.1, target nodes may be thought of as tags, which cannot perform ranging amongst themselves but transmit periodic signals used by anchors to perform anchor-to-target ranging. Therefore, As

already

due to the lack of ranging

capability between target nodes, the usage of a numerical solution of eigen-function problems, known as Nyström method becomes necessary [ 14]. Still, in order to convert the algorithm into a tracking-like, the information given by the previous time-step is linked to the current one by a solution originally developed for simultaneous diagonalization problems [ 15]. Still section 2.1 shows how the Classical MDS technique constructs a map in a Euclidean space that corresponds to the distances provided by the EDM D[n ×n]. This is done making use of the relation between the Euclidean distance matrix (EDM) and the Gram matrix, defined by: normaluperBleft-parenthsi trght-parenthsi equalseft-bracketSubscriptnormaluperXSub scriptuperNSub SubscriptmSub scriptSub persciptuperTSubscriptlef-parenthsi trght-parenthsi normaluperXSub scriptuperNSub SubscriptSub scriptSub SubscriptaSub script mesSubscriptnormaluperXSub scriptuperNSub SubscriptmSub scriptSubscriptlef-parenthsi trght-parenthsi normaluperXSub scriptuperNSub SubscriptmSub scriptSub persciptuperTSubscriptlef-parenthsi trght-parenthsi SupersciptnormaluperXSuperSubscriptuperNSuperSub scriptSuperSubscriptSuperSub scriptaSuperSubscriptSupersciptnormaluperXSuperSubscriptuperNSuperSub scriptSuperSubscriptSuperSub scriptaSuperSubscriptSuperSupersciptuperTSupersciptnormaluperXSuperSubscriptuperNSuperSub scriptaSuperSubscriptSuperSub scriptSuperSubscriptSupersciptnormaluperXSuperSubscriptuperMSuperSupersciptuperTSupersciptlef-parenthsi trght-parenthsi Baselin rght-bracket qualsStar2By2Matrix1stRow1stColumn ormaluperBSubscriptuperNSub scriptaSubscriptSub scriptBaselin 2dColumn ormaluperBSubscriptuperNSub scriptmBaselin eft-parenthsi trght-parenthsi 2ndRow1stColumn ormaluperBSubscriptuperNSub scriptmBaselin eft-parenthsi trght-parenthsi 2ndColumn ormaluperBSubscriptuperNSub scriptmSupersciptuperTBaselin eft-parenthsi trght-parenthsi normaluperBSubscriptuperNSub scriptaSupersciptnegative1Baselin eft-parenthsi trght-parenthsi normaluperBSubscriptuperNSub scriptmBaselin eft-parenthsi trght-parenthsi EndMatrix

with Na denoting the number of anchor nodes, Nm the number of mobile nodes and m the corresponding coordinate matrices. As shown above the Grammatrix B(t) is completely reconstructed using the observations between anchors and mobile m only. This is possible through the Nyström approximation [14], whose coefficients are computed as: normal up er B Subscript up er N Sub Subscript m Subscript Baseline equals negative one-half times period times left-parenthesis normal up er D Subscript up er N Sub Subscript a Subscript up er N Sub Subscript m Subscript Baseline plus normal up er C 1 minus normal up er C 2 minus normal up er C 3 times left-parenthesis t right-parenthesis right-parenthesis

normalup erC1equalsStartFraction1Overup erNSubscriptaSuperscript2BaselineEndFractionleft-bracketnormaleSubscriptleft-bracket1timesup erNSubSubscriptaSubscriptright-bracketBaselinetimesperiodtimestimesnormalup erDSubscriptup erNSubSubscriptaSubSuperscript2SubscriptBaselinetimesperiodtimesnormaleSubscriptleft-bracketup erNSubSubscriptaSubscript imes1right-bracketBaselineright-bracketperiodtimesnormaleSubscriptleft-bracketup erNSubSubscriptaSubscript imesup erNSubSubscriptmSubscriptright-bracketBaseline

normal up er C 2 equals StartFraction 1 Over up er N Subscript a Baseline EndFraction left-bracket up er D Subscript up er N Sub Subscript a Sub Superscript 2 Subscript Baseline period normal e Subscript left-bracket up er N Sub Subscript a Subscript imes 1 right-bracket Baseline right-bracket circled-times normal e Subscript left-bracket 1 times up er N Sub Subscript m Subscript right-bracket

normal up er C 3 equals StartFraction 1 Over up er N Subscript a Baseline EndFraction left-bracket normal e Subscript left-bracket 1 times up er N Sub Subscript a Subscript Sub Subscript Subscript right-bracket Baseline period times normal up er D Subscript up er N Sub Subscript a Subscript up er N Sub Subscript m Subscript Baseline left-parenthesi t right-parenthesi right-bracket circled-times normal e Subscript left-bracket up er N Sub Subscript a Subscript imes 1 right-bracket Baseline times period times

Therefore, the Nyström approximation is used

circumnavigate the EDM incompleteness. important ranging errors, the is not an Nyström approximation approximation anymore, being exact. For details refer please refer to [ 14] and references therein. Now that incompleteness problem on the EDM has been dealt with by the Nyström approximation, since a Classical MDS solution for the tracking problem requires repetitive eigen-decompostions, it is It is

to

to stress that in absence of

necessary to explain how to link the EDMs measured at different/subsequent timesteps. This is done by a Jacobian like eigen-spectrum technique which performs iterative eigen-decompostions through orthogonal similarity transformations. Defining with m as a set of matrices that can be jointly diagonalized though the similarity transformations

m with mization

m

as

, the inner

min

plane

rotation

solving

the

following

mini-

and m

problem , the off-diagonal elements of the matrix. Using the Jacobian like jointdiagonalization technique described in [ 15], it is possible to compute the rotation angle m in closed form, regardless of the symmetry properties of the matrices. It is clear that driving the minimization problem to zero, the diagonalization (eigendecomposition) is exact. This same technique can be applied to compute the eigenspectrum of a single matrix. Indeed considering B1 and B2 as the Gram matrices to eigen-decompose at two successive time steps, this joint-diagonalization technique can be used as an eigen-spectrum-tracking algorithm as follow. It is assumed that these two matrices are closely related, such that their eigen-spectra are similar, which can be considered correct and proved through the results in [ 11 ], and anyway m

m

obvious for the

case under consideration since B1 = B(t) and B2 B(t + △t). Thus, letting V(t) be the solution provided by the algorithm for B(t), namely V(t) L(t) V(t)T = B(t) with V(t) representing the product of all the Givens rotations necessary to diagonalize B(t). Then at time t + △t, feeding the algorithm with V(t) B(t + △t) • V(t)T as input, and computing the eigen-decomposition for B(t + △t), as proved in [ 10], corresponds to jump-starting the algorithm with a “good guess” of the solution, leading to faster convergence. Due to the limited noise•

=

•

•

tracking technique, a pre-filtering block could be sensibility to noisy observations. In [ 12] the application of a Wavelet-base pre-filtering technique to the MDS-based tracking algorithm just mentioned has been proved to improve the robustness of the technique even for harsh environments, namely subjected to Line of Sight/Non Line of Sight (LoS/NLoS) filtering capability

for the MDS

necessary to decrease its

conditions.

3.3. Least Square Scaling for Localization In the context of localization, a meshed network topology is considered. Such a network can be assumed to consist of N devices, deployed in a η-dimensional space. Let Na and Nm = N − Na be the number of anchor and target nodes, respectively. An anchor is a node whose location is known a priori, while a target is a node whose position is yet to be determined. Nodes are labeled with a unique number i from 1 to N. For simplicity, labels from 1 to Na and from Na + 1 to N are used for anchors and targets, respectively. Nodes are characterized by an omni-directional antenna and fixed transmission power PMAX, or equivalently, a maximum radio range RMAX. The connectivity

amongst the nodes is, then conditioned from the aforementioned values. Specifically, a node i and j are connected if the Euclidean distance dij ≤ RMAX. Moreover, if two nodes are connected, it is assumed that a distance measurement is available for the link (i, j). The particular problem of localization is strongly dependent on the amount and how “well” the connectivity is distributed. Recent results by Hendrickson and Eren et al. [16], [17] prove that there are conditions sufficient and necessary to uniquely localize a network in a 2-dimensional case, while still open is the issue for the 3-space. Theorem: Let G G(V, E) be a graph representing the network in 2-dimensional where V = {νi} and E = {eij} indicate the set of nodes and the set of connections space, nodes, amongst respectively. Let G' = G(V, E') be the augmented graph of G, so that there exist connections amongst the anchor nodes. The network is uniquely localizable if G' is 3-vertex-connected and redundantly rigid in R2. =

The aforementioned theorem provides a powerful tool, based only on combinatorial concepts, to identify the uniqueness of the solution for the localization problem. For an interested reader, we recommend the following references [16–20]. Once that the localization problem is tested to be uniquely solvable, then applying an MDS-based algorithm allows, as already discussed in section 2.1, to estimates the location of the nodes up to rigid motions, i.e. rotation, scaling, mirroring and translation. The absolute orientation can be computed by procrustes transformation. The Least Square Scaling, introduced in section 2.2, is the most suitable method for the considered localization problem. It allows to formulate the problem by a stress function that is robust to noise and incompletion thanks to the presence of weights. In literature, different methods to optimize the same stress function are proposed. The most powerful, but nevertheless more complex, are those ones based on semi-definite programming (SDP) [21] and simulated annealing (SA) [22]. In contrast, the optimization based on Newtonian gradient descent methods, such as the weighted least square (WLS) [23] and global distance continuation (GDC) [24], are less complex and sufficiently accurate. Despite the optimization technique, that in somewhat has its importance in the search of the minimum of the cost function, the efficiency of the least square scaling formulation relies on the method used to assign the weight. The firsts to identify the importance of such weights were Wolckovicz et al, in [21 ]. It was only conjectured that the weights are related to the “importance" 0 is given of the corresponding distance observation. Specifically, a weight wi,j 0 corresponds to a reliable value of to an unmeasured link, and a weight wi,j the observation for di,j. The optimum choice of such weights has not been defined yet, only heuristic methods, more or less robust, can be found in literature [25 27 ]. Amongst them the more efficient is the formulation proposed in [27 ], [28 ], where the weight is derived in a non-parametric way and it is posed in terms of a statistical =

-

confidence.

The challenge increases when the weight needs to consider the effects of random channel conditions, which can arbitrarily be in line-of-sight (LoS) or non-line-ofsight (NLoS). Such a problem has been considered for the first time in [28 ], where an hypothesis testing formulation aids the detection of NLoS conditions and gives a score to the inference of strong bias in the measurements. Finally, the WLS formulation of the Least Square Scaling is proposed to show the typical performance of a localization algorithm. More detailed information is provided in [23 ], [27 ], [28 ]. The stress function in the WLS is defined as ModifyingAbove normal up er X With ˆ equals arg times min double-vertical-bar normal up er W ring left-parenthesis normal up er D overbar squared minus normal up er D squared left-parenthesis normal up er X right-parenthesis right-parenthesis double-vertical-bar Subscript up er F Superscript 2

where W is the

weight matrix, m indicates a matrix containing the values of the average of M distance observations, the superscript 2 indicates that the element of the matrix are point-wise squared, D2 is a function of the variables X that returns the squared Euclidean distances, o denotes the Eladamard product and m is the

Frobenius norm. The weights are a derived as the confidence that the entry in m is in LoS conditions and it differs from the true value for an error of ±γ. Such weights are

given by

w Subscript i comma j Baseline times equals StartLayout Enlarged left-brace 1st Row up er P left-parenthesis d Subscript i comma j Baseline minus gamma les -than-or-equal-to d overbar Subscript i comma j times Baseline les -than-or-equal-to d Subscript i comma j Baseline plus gamma right-parenthesis equals up er P left-parenthesis left-parenthesis i comma j right-parenthesis times normal i normal s times normal up er L normal o normal up er S right-parenthesis comma for-al left-parenthesis i comma j right-parenthesis element-of up er E 2nd Row 0 times comma otherwise EndLayout

w Subscript i comma j Superscript p Baseline equals up er P left-parenthesi d Subscript i comma j Baseline minus gamma les -than-or-equal-to d overbar Subscript i comma j Baseline les -than-or-equal-to d Subscript i comma j Baseline plus gamma right-parenthesi almost-equals 1 minus 2 normal g left-parenthesi 1 minus StartFraction 1 Over StartRo t 2 pi EndRo t EndFraction integral Subscript minus infinity Superscript gamma StartFraction StartRo t up er M Subscript i j Baseline EndRo t Over sigma Subscript d i j Baseline EndFraction Baseline e Superscript minus StartFraction t squared Over 2 EndFraction Baseline normal d normal t right-parenthesi

w Subscript i j Superscript Baseline quals up er P left-parenthesi left-parenthesi i com a j right-parenthesi times normal i normal s times normal up er L normal up er O normal up er S right-parenthesi almost-equals min Underscript k Endscripts times left-parenthesi 1 minus StartFraction 1 Over StartRo t 2 pi EndRo t EndFraction integral Subscript StartFraction ModifyingAbove u With minus normal g StartRo t up er P Subscript i j com a k Baseline EndRo t Over sigma Subscript u Sub Subscript i j com a k Subscript Baseline EndFraction Superscript plus infinty Baseline Superscript minus StartFraction z squared Over 2 EndFraction Baseline normal d normal z right-parenthesi com a for-al k times uch that left-parenthesi e Subscript i k Baseline com a e Subscript j k Baseline right-parenthesi el ment-of up er E

where Mij is the number of observation for di,j, is the sample standard deviation computed for the set of measurement of di,j, Pij,k is the number of a mixed set of are the distance measurement related to the links (i, j), (i, k) and (j, k), m sample mean and the sample standard deviation related to the observations on (i, j), (i, k) and (j, k). Details and derivation of such weights are shown in [27 ], [28 ]. Finally, chosen an optimization based on quasi-newtonian LevenbergMarquadart method with close-form of the Jacobian [29], the typical performance the Least Square Scaling algorithm are proved to be robust to noise, bias and incompletion [23 ], [28 ]. m

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Localization in Ad Hoc Networks for Mobile Ubiquitous Service Provisioning Yong Bai1, Lan Chen DoCoMo Beijing Communications Laboratories Co., Ltd, Beijng, China Abstract. It is envisioned that mobile ubiquitous services can be provisioned For mobile users by the collaboration of local area networks, mobile cellular network and Internet. Specifically, it is of paramount importance to obtain node positions in ad hoc networks for locationbased context-aware services. Hop-count based localization provides a low-cost and efficient approach to yield the node locations with moderate accuracy. In this chapter, an enhanced hop-count based localization algorithm, Segmentation-aided and Density-aware Hop-count (SDH), is proposed to improve the estimation accuracy. In the proposed scheme, the path from one node to the reference nodes (RNs) is first divided into several three-hop segments; each segment distance can be estimated by density-aware hop-count localization. Based on the proposed SDH localization algorithm, we further propose a relative location estimation method for one mobile node to reach the interested node without knowing the location map of whole network. The advantages Of the proposed scheme over other conventional schemes are verified by numerical analysis and simulation.

Keywords: localization, mobile cellular network, ad hoc network, 4G.

1. Introduction It is envisioned that mobile ubiquitous services can be provisioned by the collaboration of local area networks, mobile cellular network and Internet. It has been proposed in [ 1 ] to expand B3G/4G mobile cellular network to real space via local networks and mobile terminals. With both cellular and short-range radio interas the gateway for data flow with more physical information between the mobile cellular and local area networks. area

faces, mobile terminal would function

Specifically, with the aiding of location information of nodes in ad hoc networks, more location-based context-aware services in 4G era can be available for mobile users such as people and object tracking, target detection and monitoring, data aggregation, sensor query, position-based routing, etc. For such service provisioning, the spatial localization techniques are needed to obtain the absolute positions of nodes and relative positions between nodes in ad hoc networks. As shown in Figure 1, the mobile user with mobile terminal needs to know the position of one node (e.g., S) in the local ad hoc network. However, localization in ad hoc networks is a challenging task. Location-sensing units such as GPS are too expensive to be equipped on a large number of ad hoc nodes. Even with GPS units,

1 Yong Bai, DoCoMo Beijing Communications Laboratories Co., Ltd, 7/F, Raycom Infotech Park Tower A, No.2 Kexueyuan South Road, Haidian District, Beijing, 100080 P.R. China. Email:bai@ docomolabs-beijing.com.cn

DOI: 10.1201/9781003336853-29

Localization in Ad Hoc Networks

Figure 1. Application scenario

additional efforts are needed for indoor positioning of ad hoc nodes. It is also not practical for range-based localization algorithms that exploit measured Received Signal Strength Indication (RSSI) and signal propagation characteristics. The radio propagation conditions in ad hoc networks are dynamic due to shadowing, fading, and scattering. Hence the attenuation of RF signals is not consistent with respect to distance. Therefore, GPS-free and range-free localization algorithms are more promising in such a networking environment. The range-free localization algorithms such as DV-Hop [2 ] and DHL [3 ][ 4 ] use hop-counts to reference nodes (RNs) of known positions as a substitute to physical distance estimates. It is a low-cost approach to yield moderate position accuracy. In order to transform hop counts into approximate distances, the system must estimate the average distance corresponding to a hop, i.e., hop-distance. In hop-count based localization algorithms, the hop-distance of the paths between the interested node and RNs needs to know in the first phase before performing triangulation location computation. The average hop-distance of the twisted path between the interested node and RNs is relevant to network density and node distribution. To provide more accurate distance estimation for hop-count based localization algorithms, we observe that large distance estimation error is prone to occur when the hopcount of the twisted path exceeds three. We also analyze the impacts of network density and node distribution on the distance estimation. Based on our observation and analysis, we propose a Segmentation-Aided and Density-aware Hop-Count (SDH) localization algorithm [6 ]. In the proposed algorithm, the path between the interested node and one RN is divided into segments that have three hops. Subsequently, the segment-count and the segment distances are utilized to obtain more accurate distance estimation of the whole twisted path. In the context-aware applications such as object tracking and object reaching, a mobile user may need to know the relative distance of one certain node and moves toward that node according to estimated relative orientation. With the estimated absolute locations of individual nodes, the relative location between nodes can be estimated thereafter. One relative location algorithm has been presented in [5] to

2. Related Work

provide directional neighbor localization in a network-wide coordinate system. For instance, when the mobile user carries the mobile node, the mobile user may face any direction and he is able to decide its moving direction to get closer to the interested node when the coordinates and the network topology are reconstructed to him. However, it may not be possible to show the whole network topology and coordinates on a mobile terminal with the limited-screen size. To address this issue, we propose one algorithm to designate the relative location for one mobile user to reach another node step by step without the need to know the network-wide coordinate system and the location map of all network nodes [6]. The rest of the chapter is organized as follows. Section 2 reviews related work on hop-count based localization algorithms. Section 3 presents our proposed SDH localization algorithm. Section 4 presents our proposed relative localization algorithm for mobile nodes. Simulation results for performance evaluation are given in Section 5. Finally, conclusions are made in Section 6.

2. Related Work In a 2D (or 3D) ad hoc network, it is assumed that at least three RNs are deployed with either known priori location information or self positioning functions enabled by GPS or other localization elements. Other nodes can first estimate their distances to the RNs and then determine their locations by using distance computation method such as triangulation algorithm.

As a low-cost solution, the distance between one node and a RN can be estimated by the product of hop-count from the RN and the transmission range, i.e., D = HC × R, where D is the distance from the RN, HC is the hop-count from the RN and R is the transmission range. DV-Hop localization algorithm [2 ] uses average distance per hop-count,Ravg, to account for the over-estimation in sparse network. Thus, the estimated distance from RN is D = HC x Ravg instead of D HC x R. This algorithm yields good performance in uniform distributed network. However, in a non-uniform distributed =

network with a combination of dense and sparse regions, the use of Ravg actually shows degraded performance since the distance traversed for each hop is no longer consistent. Therefore, a drawback of DV-Hop is that it fails for highly irregular network topologies, where the variance in actual hop-distance is very large.

Another hop-count localization algorithm, Density-Aware Hop-Count Localization (DHL) [3][4], does not require network-wide uniformity. The neighbors of a node are distributed randomly surrounding the node. For simplicity, the degree of a node (i.e., the number of neighboring nodes), γ , is used to represent local density. Range ratio, μ(0